Skip to contents

A function to compute joint-count test for binomial and multinomial (asymptotic and permutation distributions).

jc.test.Rd

A function to compute joincount tests for spatial qualitative data. This function is a wrapper of joincount.multi and joincount.test in spdep package.

Usage

jc.test(formula = NULL,
               data = NULL,
               fx = NULL,
               listw = NULL,
               na.action,
               zero.policy = NULL,
               distr = "asymptotic",
               alternative = "greater",
               control =list())

Arguments

formula

a symbolic description of the factor(s).

data

an (optional) data frame or a sf object with points/multipolygons geometry containing the variable(s) to be tested.

fx

a factor or a matrix of factors in columns

listw

A listw object created for example by nb2listw from spdep package; if nb2listw not given, the spatial weights are built using the object given in listw argument (usually an sf object). Default = NULL.

na.action

A function (default options("na.action")), can also be na.omit or na.exclude. It may be necessary to set zero.policy to TRUE because this subsetting may create no-neighbour observations.

zero.policy

Similar to the corresponding parameter of lagsarlm function in spatialreg package. If TRUE assign zero to the lagged value of zones without neighbours. Default = NULL.

distr

character. Distribution type "asymptotic" (default) or "mc".

alternative

character string specifying the alternative hypothesis, must be one of "greater" (default), or "less".

control

list of additional arguments.

Value

An spjctest object. This type of object is a list of htest objects. The length of the list is the number of factor variables included in the formula or the number of columns in fx. Each element of the list can be a jclist object, for binomial factors, or a jcmulti object for multinomial factors. See joincount.test or joincount.multi for additional details.

Control arguments

nsimnumber of permutations used in the Monte Carlo distribution. Default nsim = 999.
seedinitseed to select the initial element during the simulations. Default seedinit = 1111.
adjust.ndefault *TRUE*, if *FALSE* the number of observations is not adjusted for no-neighbour observations, if *TRUE*, the number of observations is adjusted consistently. See joincount.multi for aditional information.
spChkshould the data vector names be checked against the spatial objects for identity integrity, *TRUE*, or *FALSE*, default *NULL* to use *get.spChkOption()*. See joincount.multi for aditional information.
samplingdefault *nonfree*, may be *free*. See joincount.test for additional information.
queendefault *TRUE*. Defines the neighborhood criteria for *sf* objects.
styledefines the style for listw. Default = *B* (binary).
knnchooses the number of neighboors when this criteria is used. Default knn = 5.

References

  • Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, pp. 19-20.

  • Upton, G., Fingleton, B. 1985 Spatial data analysis by example: point pattern and qualitative data, Wiley, pp. 158–170.

See also

print.summary.spqtest, joincount.test, joincount.multi

Author

Fernando Lópezfernando.lopez@upct.es
Román Mínguezroman.minguez@uclm.es
Antonio Páezpaezha@gmail.com
Manuel Ruizmanuel.ruiz@upct.es

Examples


## Case 1
## Multinomial + Binomial using a sf multipolygon
# \donttest{
data("provinces_spain")
sf::sf_use_s2(FALSE)
provinces_spain$Male2Female <- factor(provinces_spain$Male2Female > 100)
levels(provinces_spain$Male2Female) = c("men","woman")
provinces_spain$Older <- cut(provinces_spain$Older, breaks = c(-Inf,19,22.5,Inf))
levels(provinces_spain$Older) = c("low","middle","high")
f1 <- ~ Older + Male2Female
jc1 <- jc.test(formula = f1,
               data = provinces_spain,
               distr = "mc",
               alternative = "greater",
               zero.policy = TRUE)
#> although coordinates are longitude/latitude, st_intersects assumes that they are planar
summary(jc1)
#> <div id="rgrdpswsrb" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
#>   <style>html {
#>   font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
#> }
#> 
#> #rgrdpswsrb .gt_table {
#>   display: table;
#>   border-collapse: collapse;
#>   margin-left: auto;
#>   margin-right: auto;
#>   color: #333333;
#>   font-size: 16px;
#>   font-weight: normal;
#>   font-style: normal;
#>   background-color: #FFFFFF;
#>   width: auto;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #A8A8A8;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #A8A8A8;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#> }
#> 
#> #rgrdpswsrb .gt_heading {
#>   background-color: #FFFFFF;
#>   text-align: center;
#>   border-bottom-color: #FFFFFF;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #rgrdpswsrb .gt_title {
#>   color: #333333;
#>   font-size: 125%;
#>   font-weight: initial;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-color: #FFFFFF;
#>   border-bottom-width: 0;
#> }
#> 
#> #rgrdpswsrb .gt_subtitle {
#>   color: #333333;
#>   font-size: 85%;
#>   font-weight: initial;
#>   padding-top: 0;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-color: #FFFFFF;
#>   border-top-width: 0;
#> }
#> 
#> #rgrdpswsrb .gt_bottom_border {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #rgrdpswsrb .gt_col_headings {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #rgrdpswsrb .gt_col_heading {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   overflow-x: hidden;
#> }
#> 
#> #rgrdpswsrb .gt_column_spanner_outer {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   padding-top: 0;
#>   padding-bottom: 0;
#>   padding-left: 4px;
#>   padding-right: 4px;
#> }
#> 
#> #rgrdpswsrb .gt_column_spanner_outer:first-child {
#>   padding-left: 0;
#> }
#> 
#> #rgrdpswsrb .gt_column_spanner_outer:last-child {
#>   padding-right: 0;
#> }
#> 
#> #rgrdpswsrb .gt_column_spanner {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 5px;
#>   overflow-x: hidden;
#>   display: inline-block;
#>   width: 100%;
#> }
#> 
#> #rgrdpswsrb .gt_group_heading {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #rgrdpswsrb .gt_empty_group_heading {
#>   padding: 0.5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #rgrdpswsrb .gt_from_md > :first-child {
#>   margin-top: 0;
#> }
#> 
#> #rgrdpswsrb .gt_from_md > :last-child {
#>   margin-bottom: 0;
#> }
#> 
#> #rgrdpswsrb .gt_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   margin: 10px;
#>   border-top-style: solid;
#>   border-top-width: 1px;
#>   border-top-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#>   overflow-x: hidden;
#> }
#> 
#> #rgrdpswsrb .gt_stub {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #rgrdpswsrb .gt_stub_row_group {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   vertical-align: top;
#> }
#> 
#> #rgrdpswsrb .gt_row_group_first td {
#>   border-top-width: 2px;
#> }
#> 
#> #rgrdpswsrb .gt_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #rgrdpswsrb .gt_first_summary_row {
#>   border-top-style: solid;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #rgrdpswsrb .gt_first_summary_row.thick {
#>   border-top-width: 2px;
#> }
#> 
#> #rgrdpswsrb .gt_last_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #rgrdpswsrb .gt_grand_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #rgrdpswsrb .gt_first_grand_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-style: double;
#>   border-top-width: 6px;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #rgrdpswsrb .gt_striped {
#>   background-color: rgba(128, 128, 128, 0.05);
#> }
#> 
#> #rgrdpswsrb .gt_table_body {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #rgrdpswsrb .gt_footnotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #rgrdpswsrb .gt_footnote {
#>   margin: 0px;
#>   font-size: 90%;
#>   padding-left: 4px;
#>   padding-right: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #rgrdpswsrb .gt_sourcenotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #rgrdpswsrb .gt_sourcenote {
#>   font-size: 90%;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #rgrdpswsrb .gt_left {
#>   text-align: left;
#> }
#> 
#> #rgrdpswsrb .gt_center {
#>   text-align: center;
#> }
#> 
#> #rgrdpswsrb .gt_right {
#>   text-align: right;
#>   font-variant-numeric: tabular-nums;
#> }
#> 
#> #rgrdpswsrb .gt_font_normal {
#>   font-weight: normal;
#> }
#> 
#> #rgrdpswsrb .gt_font_bold {
#>   font-weight: bold;
#> }
#> 
#> #rgrdpswsrb .gt_font_italic {
#>   font-style: italic;
#> }
#> 
#> #rgrdpswsrb .gt_super {
#>   font-size: 65%;
#> }
#> 
#> #rgrdpswsrb .gt_footnote_marks {
#>   font-style: italic;
#>   font-weight: normal;
#>   font-size: 75%;
#>   vertical-align: 0.4em;
#> }
#> 
#> #rgrdpswsrb .gt_asterisk {
#>   font-size: 100%;
#>   vertical-align: 0;
#> }
#> 
#> #rgrdpswsrb .gt_slash_mark {
#>   font-size: 0.7em;
#>   line-height: 0.7em;
#>   vertical-align: 0.15em;
#> }
#> 
#> #rgrdpswsrb .gt_fraction_numerator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: 0.45em;
#> }
#> 
#> #rgrdpswsrb .gt_fraction_denominator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: -0.05em;
#> }
#> </style>
#>   <table class="gt_table">
#>   <thead class="gt_header">
#>     <tr>
#>       <th colspan="5" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>JoinCount Spatial Tests (Monte Carlo)</th>
#>     </tr>
#>     
#>   </thead>
#>   <thead class="gt_col_headings">
#>     <tr>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">pairs</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">pvalue</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Joincount</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Expected</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Variance</th>
#>     </tr>
#>   </thead>
#>   <tbody class="gt_table_body">
#>     <tr class="gt_group_heading_row">
#>       <td colspan="5" class="gt_group_heading">Older - multinomial - alternative: greater - Monte-Carlo simulation of
#>         join-count statistic (nonfree sampling)</td>
#>     </tr>
#>     <tr class="gt_row_group_first"><td class="gt_row gt_left">high:high</td>
#> <td class="gt_row gt_right">0.44100</td>
#> <td class="gt_row gt_right">14</td>
#> <td class="gt_row gt_right">13.99</td>
#> <td class="gt_row gt_right">11.06</td></tr>
#>     <tr><td class="gt_row gt_left">low:low</td>
#> <td class="gt_row gt_right">0.69700</td>
#> <td class="gt_row gt_right">7</td>
#> <td class="gt_row gt_right">8.31</td>
#> <td class="gt_row gt_right">6.57</td></tr>
#>     <tr><td class="gt_row gt_left">middle:middle</td>
#> <td class="gt_row gt_right">0.54900</td>
#> <td class="gt_row gt_right">13</td>
#> <td class="gt_row gt_right">13.83</td>
#> <td class="gt_row gt_right">10.44</td></tr>
#>     <tr><td class="gt_row gt_left">low:high</td>
#> <td class="gt_row gt_right">0.35800</td>
#> <td class="gt_row gt_right">24</td>
#> <td class="gt_row gt_right">22.88</td>
#> <td class="gt_row gt_right">15.87</td></tr>
#>     <tr><td class="gt_row gt_left">middle:high</td>
#> <td class="gt_row gt_right">0.57000</td>
#> <td class="gt_row gt_right">28</td>
#> <td class="gt_row gt_right">29.15</td>
#> <td class="gt_row gt_right">20.45</td></tr>
#>     <tr><td class="gt_row gt_left">middle:low</td>
#> <td class="gt_row gt_right">0.30300</td>
#> <td class="gt_row gt_right">25</td>
#> <td class="gt_row gt_right">22.83</td>
#> <td class="gt_row gt_right">17.09</td></tr>
#>     <tr><td class="gt_row gt_left">Jtot</td>
#> <td class="gt_row gt_right">0.38300</td>
#> <td class="gt_row gt_right">77</td>
#> <td class="gt_row gt_right">74.86</td>
#> <td class="gt_row gt_right">23.27</td></tr>
#>     <tr class="gt_group_heading_row">
#>       <td colspan="5" class="gt_group_heading">Male2Female - binomial - alternative: greater - Monte-Carlo simulation of join-count statistic</td>
#>     </tr>
#>     <tr class="gt_row_group_first"><td class="gt_row gt_left">men-men</td>
#> <td class="gt_row gt_right">0.55100</td>
#> <td class="gt_row gt_right">60</td>
#> <td class="gt_row gt_right">60.62</td>
#> <td class="gt_row gt_right">22.64</td></tr>
#>     <tr><td class="gt_row gt_left">woman-woman</td>
#> <td class="gt_row gt_right">0.01500</td>
#> <td class="gt_row gt_right">13</td>
#> <td class="gt_row gt_right">6.98</td>
#> <td class="gt_row gt_right">5.89</td></tr>
#>   </tbody>
#>   
#>   
#> </table>
#> </div>

provinces_spain$Coast <- factor(provinces_spain$Coast)
levels(provinces_spain$Coast) = c("no","yes")
f2 <- ~ Male2Female + Coast
jc2 <- jc.test(formula = f2,
               data = provinces_spain,
               distr = "mc",
               zero.policy = TRUE)
#> although coordinates are longitude/latitude, st_intersects assumes that they are planar
summary(jc2)
#> <div id="krjaggrbnb" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
#>   <style>html {
#>   font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
#> }
#> 
#> #krjaggrbnb .gt_table {
#>   display: table;
#>   border-collapse: collapse;
#>   margin-left: auto;
#>   margin-right: auto;
#>   color: #333333;
#>   font-size: 16px;
#>   font-weight: normal;
#>   font-style: normal;
#>   background-color: #FFFFFF;
#>   width: auto;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #A8A8A8;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #A8A8A8;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#> }
#> 
#> #krjaggrbnb .gt_heading {
#>   background-color: #FFFFFF;
#>   text-align: center;
#>   border-bottom-color: #FFFFFF;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #krjaggrbnb .gt_title {
#>   color: #333333;
#>   font-size: 125%;
#>   font-weight: initial;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-color: #FFFFFF;
#>   border-bottom-width: 0;
#> }
#> 
#> #krjaggrbnb .gt_subtitle {
#>   color: #333333;
#>   font-size: 85%;
#>   font-weight: initial;
#>   padding-top: 0;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-color: #FFFFFF;
#>   border-top-width: 0;
#> }
#> 
#> #krjaggrbnb .gt_bottom_border {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #krjaggrbnb .gt_col_headings {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #krjaggrbnb .gt_col_heading {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   overflow-x: hidden;
#> }
#> 
#> #krjaggrbnb .gt_column_spanner_outer {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   padding-top: 0;
#>   padding-bottom: 0;
#>   padding-left: 4px;
#>   padding-right: 4px;
#> }
#> 
#> #krjaggrbnb .gt_column_spanner_outer:first-child {
#>   padding-left: 0;
#> }
#> 
#> #krjaggrbnb .gt_column_spanner_outer:last-child {
#>   padding-right: 0;
#> }
#> 
#> #krjaggrbnb .gt_column_spanner {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 5px;
#>   overflow-x: hidden;
#>   display: inline-block;
#>   width: 100%;
#> }
#> 
#> #krjaggrbnb .gt_group_heading {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #krjaggrbnb .gt_empty_group_heading {
#>   padding: 0.5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #krjaggrbnb .gt_from_md > :first-child {
#>   margin-top: 0;
#> }
#> 
#> #krjaggrbnb .gt_from_md > :last-child {
#>   margin-bottom: 0;
#> }
#> 
#> #krjaggrbnb .gt_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   margin: 10px;
#>   border-top-style: solid;
#>   border-top-width: 1px;
#>   border-top-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#>   overflow-x: hidden;
#> }
#> 
#> #krjaggrbnb .gt_stub {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #krjaggrbnb .gt_stub_row_group {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   vertical-align: top;
#> }
#> 
#> #krjaggrbnb .gt_row_group_first td {
#>   border-top-width: 2px;
#> }
#> 
#> #krjaggrbnb .gt_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #krjaggrbnb .gt_first_summary_row {
#>   border-top-style: solid;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #krjaggrbnb .gt_first_summary_row.thick {
#>   border-top-width: 2px;
#> }
#> 
#> #krjaggrbnb .gt_last_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #krjaggrbnb .gt_grand_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #krjaggrbnb .gt_first_grand_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-style: double;
#>   border-top-width: 6px;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #krjaggrbnb .gt_striped {
#>   background-color: rgba(128, 128, 128, 0.05);
#> }
#> 
#> #krjaggrbnb .gt_table_body {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #krjaggrbnb .gt_footnotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #krjaggrbnb .gt_footnote {
#>   margin: 0px;
#>   font-size: 90%;
#>   padding-left: 4px;
#>   padding-right: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #krjaggrbnb .gt_sourcenotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #krjaggrbnb .gt_sourcenote {
#>   font-size: 90%;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #krjaggrbnb .gt_left {
#>   text-align: left;
#> }
#> 
#> #krjaggrbnb .gt_center {
#>   text-align: center;
#> }
#> 
#> #krjaggrbnb .gt_right {
#>   text-align: right;
#>   font-variant-numeric: tabular-nums;
#> }
#> 
#> #krjaggrbnb .gt_font_normal {
#>   font-weight: normal;
#> }
#> 
#> #krjaggrbnb .gt_font_bold {
#>   font-weight: bold;
#> }
#> 
#> #krjaggrbnb .gt_font_italic {
#>   font-style: italic;
#> }
#> 
#> #krjaggrbnb .gt_super {
#>   font-size: 65%;
#> }
#> 
#> #krjaggrbnb .gt_footnote_marks {
#>   font-style: italic;
#>   font-weight: normal;
#>   font-size: 75%;
#>   vertical-align: 0.4em;
#> }
#> 
#> #krjaggrbnb .gt_asterisk {
#>   font-size: 100%;
#>   vertical-align: 0;
#> }
#> 
#> #krjaggrbnb .gt_slash_mark {
#>   font-size: 0.7em;
#>   line-height: 0.7em;
#>   vertical-align: 0.15em;
#> }
#> 
#> #krjaggrbnb .gt_fraction_numerator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: 0.45em;
#> }
#> 
#> #krjaggrbnb .gt_fraction_denominator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: -0.05em;
#> }
#> </style>
#>   <table class="gt_table">
#>   <thead class="gt_header">
#>     <tr>
#>       <th colspan="5" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>JoinCount Spatial Tests (Monte Carlo)</th>
#>     </tr>
#>     
#>   </thead>
#>   <thead class="gt_col_headings">
#>     <tr>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">pairs</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">pvalue</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Joincount</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Expected</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Variance</th>
#>     </tr>
#>   </thead>
#>   <tbody class="gt_table_body">
#>     <tr class="gt_group_heading_row">
#>       <td colspan="5" class="gt_group_heading">Male2Female - binomial - alternative: greater - Monte-Carlo simulation of join-count statistic</td>
#>     </tr>
#>     <tr class="gt_row_group_first"><td class="gt_row gt_left">men-men</td>
#> <td class="gt_row gt_right">0.52200</td>
#> <td class="gt_row gt_right">60</td>
#> <td class="gt_row gt_right">60.46</td>
#> <td class="gt_row gt_right">22.66</td></tr>
#>     <tr><td class="gt_row gt_left">woman-woman</td>
#> <td class="gt_row gt_right">0.01000</td>
#> <td class="gt_row gt_right">13</td>
#> <td class="gt_row gt_right">6.96</td>
#> <td class="gt_row gt_right">5.66</td></tr>
#>     <tr class="gt_group_heading_row">
#>       <td colspan="5" class="gt_group_heading">Coast - binomial - alternative: greater - Monte-Carlo simulation of join-count statistic</td>
#>     </tr>
#>     <tr class="gt_row_group_first"><td class="gt_row gt_left">no-no</td>
#> <td class="gt_row gt_right">0.00100</td>
#> <td class="gt_row gt_right">64</td>
#> <td class="gt_row gt_right">36.62</td>
#> <td class="gt_row gt_right">22.03</td></tr>
#>     <tr><td class="gt_row gt_left">yes-yes</td>
#> <td class="gt_row gt_right">0.90450</td>
#> <td class="gt_row gt_right">14</td>
#> <td class="gt_row gt_right">18.84</td>
#> <td class="gt_row gt_right">14.13</td></tr>
#>   </tbody>
#>   
#>   
#> </table>
#> </div>
# }

# Case 2:
## Multinomial using a sf multipoint
data("FastFood.sf")
sf::sf_use_s2(FALSE)
f1 <- ~ Type
jc3 <- jc.test(formula = f1,
               data = FastFood.sf,
               distr = "asymptotic",
               control = list(knn = 6))
#> Warning: bounding box has potentially an invalid value range for longlat data
#> Warning: bounding box has potentially an invalid value range for longlat data
#> Warning: knearneigh: coordinates are not geographical: longlat argument wrong
 summary(jc3)
#> <div id="ltmvkjwapz" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
#>   <style>html {
#>   font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
#> }
#> 
#> #ltmvkjwapz .gt_table {
#>   display: table;
#>   border-collapse: collapse;
#>   margin-left: auto;
#>   margin-right: auto;
#>   color: #333333;
#>   font-size: 16px;
#>   font-weight: normal;
#>   font-style: normal;
#>   background-color: #FFFFFF;
#>   width: auto;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #A8A8A8;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #A8A8A8;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#> }
#> 
#> #ltmvkjwapz .gt_heading {
#>   background-color: #FFFFFF;
#>   text-align: center;
#>   border-bottom-color: #FFFFFF;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #ltmvkjwapz .gt_title {
#>   color: #333333;
#>   font-size: 125%;
#>   font-weight: initial;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-color: #FFFFFF;
#>   border-bottom-width: 0;
#> }
#> 
#> #ltmvkjwapz .gt_subtitle {
#>   color: #333333;
#>   font-size: 85%;
#>   font-weight: initial;
#>   padding-top: 0;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-color: #FFFFFF;
#>   border-top-width: 0;
#> }
#> 
#> #ltmvkjwapz .gt_bottom_border {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #ltmvkjwapz .gt_col_headings {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #ltmvkjwapz .gt_col_heading {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   overflow-x: hidden;
#> }
#> 
#> #ltmvkjwapz .gt_column_spanner_outer {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   padding-top: 0;
#>   padding-bottom: 0;
#>   padding-left: 4px;
#>   padding-right: 4px;
#> }
#> 
#> #ltmvkjwapz .gt_column_spanner_outer:first-child {
#>   padding-left: 0;
#> }
#> 
#> #ltmvkjwapz .gt_column_spanner_outer:last-child {
#>   padding-right: 0;
#> }
#> 
#> #ltmvkjwapz .gt_column_spanner {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 5px;
#>   overflow-x: hidden;
#>   display: inline-block;
#>   width: 100%;
#> }
#> 
#> #ltmvkjwapz .gt_group_heading {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #ltmvkjwapz .gt_empty_group_heading {
#>   padding: 0.5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #ltmvkjwapz .gt_from_md > :first-child {
#>   margin-top: 0;
#> }
#> 
#> #ltmvkjwapz .gt_from_md > :last-child {
#>   margin-bottom: 0;
#> }
#> 
#> #ltmvkjwapz .gt_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   margin: 10px;
#>   border-top-style: solid;
#>   border-top-width: 1px;
#>   border-top-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#>   overflow-x: hidden;
#> }
#> 
#> #ltmvkjwapz .gt_stub {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #ltmvkjwapz .gt_stub_row_group {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   vertical-align: top;
#> }
#> 
#> #ltmvkjwapz .gt_row_group_first td {
#>   border-top-width: 2px;
#> }
#> 
#> #ltmvkjwapz .gt_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #ltmvkjwapz .gt_first_summary_row {
#>   border-top-style: solid;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #ltmvkjwapz .gt_first_summary_row.thick {
#>   border-top-width: 2px;
#> }
#> 
#> #ltmvkjwapz .gt_last_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #ltmvkjwapz .gt_grand_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #ltmvkjwapz .gt_first_grand_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-style: double;
#>   border-top-width: 6px;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #ltmvkjwapz .gt_striped {
#>   background-color: rgba(128, 128, 128, 0.05);
#> }
#> 
#> #ltmvkjwapz .gt_table_body {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #ltmvkjwapz .gt_footnotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #ltmvkjwapz .gt_footnote {
#>   margin: 0px;
#>   font-size: 90%;
#>   padding-left: 4px;
#>   padding-right: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #ltmvkjwapz .gt_sourcenotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #ltmvkjwapz .gt_sourcenote {
#>   font-size: 90%;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #ltmvkjwapz .gt_left {
#>   text-align: left;
#> }
#> 
#> #ltmvkjwapz .gt_center {
#>   text-align: center;
#> }
#> 
#> #ltmvkjwapz .gt_right {
#>   text-align: right;
#>   font-variant-numeric: tabular-nums;
#> }
#> 
#> #ltmvkjwapz .gt_font_normal {
#>   font-weight: normal;
#> }
#> 
#> #ltmvkjwapz .gt_font_bold {
#>   font-weight: bold;
#> }
#> 
#> #ltmvkjwapz .gt_font_italic {
#>   font-style: italic;
#> }
#> 
#> #ltmvkjwapz .gt_super {
#>   font-size: 65%;
#> }
#> 
#> #ltmvkjwapz .gt_footnote_marks {
#>   font-style: italic;
#>   font-weight: normal;
#>   font-size: 75%;
#>   vertical-align: 0.4em;
#> }
#> 
#> #ltmvkjwapz .gt_asterisk {
#>   font-size: 100%;
#>   vertical-align: 0;
#> }
#> 
#> #ltmvkjwapz .gt_slash_mark {
#>   font-size: 0.7em;
#>   line-height: 0.7em;
#>   vertical-align: 0.15em;
#> }
#> 
#> #ltmvkjwapz .gt_fraction_numerator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: 0.45em;
#> }
#> 
#> #ltmvkjwapz .gt_fraction_denominator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: -0.05em;
#> }
#> </style>
#>   <table class="gt_table">
#>   <thead class="gt_header">
#>     <tr>
#>       <th colspan="6" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>JoinCount Spatial Tests (asymptotic)</th>
#>     </tr>
#>     
#>   </thead>
#>   <thead class="gt_col_headings">
#>     <tr>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">pairs</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">z-value</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">pvalue</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Joincount</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Expected</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Variance</th>
#>     </tr>
#>   </thead>
#>   <tbody class="gt_table_body">
#>     <tr class="gt_group_heading_row">
#>       <td colspan="6" class="gt_group_heading">Type - multinomial - alternative: greater - Join count test under nonfree sampling</td>
#>     </tr>
#>     <tr class="gt_row_group_first"><td class="gt_row gt_left">H:H</td>
#> <td class="gt_row gt_right">&minus;0.23</td>
#> <td class="gt_row gt_right">0.58942</td>
#> <td class="gt_row gt_right">255.5</td>
#> <td class="gt_row gt_right">258.05</td>
#> <td class="gt_row gt_right">127.06</td></tr>
#>     <tr><td class="gt_row gt_left">P:P</td>
#> <td class="gt_row gt_right">0.30</td>
#> <td class="gt_row gt_right">0.38114</td>
#> <td class="gt_row gt_right">317.0</td>
#> <td class="gt_row gt_right">313.38</td>
#> <td class="gt_row gt_right">143.47</td></tr>
#>     <tr><td class="gt_row gt_left">S:S</td>
#> <td class="gt_row gt_right">&minus;1.82</td>
#> <td class="gt_row gt_right">0.96574</td>
#> <td class="gt_row gt_right">283.5</td>
#> <td class="gt_row gt_right">305.14</td>
#> <td class="gt_row gt_right">141.19</td></tr>
#>     <tr><td class="gt_row gt_left">P:H</td>
#> <td class="gt_row gt_right">0.02</td>
#> <td class="gt_row gt_right">0.49358</td>
#> <td class="gt_row gt_right">571.0</td>
#> <td class="gt_row gt_right">570.72</td>
#> <td class="gt_row gt_right">304.67</td></tr>
#>     <tr><td class="gt_row gt_left">S:H</td>
#> <td class="gt_row gt_right">0.05</td>
#> <td class="gt_row gt_right">0.48128</td>
#> <td class="gt_row gt_right">564.0</td>
#> <td class="gt_row gt_right">563.18</td>
#> <td class="gt_row gt_right">301.61</td></tr>
#>     <tr><td class="gt_row gt_left">S:P</td>
#> <td class="gt_row gt_right">1.08</td>
#> <td class="gt_row gt_right">0.14022</td>
#> <td class="gt_row gt_right">640.0</td>
#> <td class="gt_row gt_right">620.53</td>
#> <td class="gt_row gt_right">325.50</td></tr>
#>     <tr><td class="gt_row gt_left">Jtot</td>
#> <td class="gt_row gt_right">0.90</td>
#> <td class="gt_row gt_right">0.18350</td>
#> <td class="gt_row gt_right">1775.0</td>
#> <td class="gt_row gt_right">1,754.43</td>
#> <td class="gt_row gt_right">519.87</td></tr>
#>   </tbody>
#>   
#>   
#> </table>
#> </div>

# Examples function joincount.test
data(oldcol, package = "spdep")
HICRIME <- cut(COL.OLD$CRIME, breaks = c(0,35,80), labels = c("low","high"))
names(HICRIME) <- rownames(COL.OLD)
jc4 <- jc.test(fx = HICRIME,
               listw = spdep::nb2listw(COL.nb,
               style="B"))
summary(jc4)
#> <div id="hbyizqonme" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
#>   <style>html {
#>   font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
#> }
#> 
#> #hbyizqonme .gt_table {
#>   display: table;
#>   border-collapse: collapse;
#>   margin-left: auto;
#>   margin-right: auto;
#>   color: #333333;
#>   font-size: 16px;
#>   font-weight: normal;
#>   font-style: normal;
#>   background-color: #FFFFFF;
#>   width: auto;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #A8A8A8;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #A8A8A8;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#> }
#> 
#> #hbyizqonme .gt_heading {
#>   background-color: #FFFFFF;
#>   text-align: center;
#>   border-bottom-color: #FFFFFF;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #hbyizqonme .gt_title {
#>   color: #333333;
#>   font-size: 125%;
#>   font-weight: initial;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-color: #FFFFFF;
#>   border-bottom-width: 0;
#> }
#> 
#> #hbyizqonme .gt_subtitle {
#>   color: #333333;
#>   font-size: 85%;
#>   font-weight: initial;
#>   padding-top: 0;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-color: #FFFFFF;
#>   border-top-width: 0;
#> }
#> 
#> #hbyizqonme .gt_bottom_border {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #hbyizqonme .gt_col_headings {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #hbyizqonme .gt_col_heading {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   overflow-x: hidden;
#> }
#> 
#> #hbyizqonme .gt_column_spanner_outer {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   padding-top: 0;
#>   padding-bottom: 0;
#>   padding-left: 4px;
#>   padding-right: 4px;
#> }
#> 
#> #hbyizqonme .gt_column_spanner_outer:first-child {
#>   padding-left: 0;
#> }
#> 
#> #hbyizqonme .gt_column_spanner_outer:last-child {
#>   padding-right: 0;
#> }
#> 
#> #hbyizqonme .gt_column_spanner {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 5px;
#>   overflow-x: hidden;
#>   display: inline-block;
#>   width: 100%;
#> }
#> 
#> #hbyizqonme .gt_group_heading {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #hbyizqonme .gt_empty_group_heading {
#>   padding: 0.5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #hbyizqonme .gt_from_md > :first-child {
#>   margin-top: 0;
#> }
#> 
#> #hbyizqonme .gt_from_md > :last-child {
#>   margin-bottom: 0;
#> }
#> 
#> #hbyizqonme .gt_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   margin: 10px;
#>   border-top-style: solid;
#>   border-top-width: 1px;
#>   border-top-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#>   overflow-x: hidden;
#> }
#> 
#> #hbyizqonme .gt_stub {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #hbyizqonme .gt_stub_row_group {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   vertical-align: top;
#> }
#> 
#> #hbyizqonme .gt_row_group_first td {
#>   border-top-width: 2px;
#> }
#> 
#> #hbyizqonme .gt_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #hbyizqonme .gt_first_summary_row {
#>   border-top-style: solid;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #hbyizqonme .gt_first_summary_row.thick {
#>   border-top-width: 2px;
#> }
#> 
#> #hbyizqonme .gt_last_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #hbyizqonme .gt_grand_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #hbyizqonme .gt_first_grand_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-style: double;
#>   border-top-width: 6px;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #hbyizqonme .gt_striped {
#>   background-color: rgba(128, 128, 128, 0.05);
#> }
#> 
#> #hbyizqonme .gt_table_body {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #hbyizqonme .gt_footnotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #hbyizqonme .gt_footnote {
#>   margin: 0px;
#>   font-size: 90%;
#>   padding-left: 4px;
#>   padding-right: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #hbyizqonme .gt_sourcenotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #hbyizqonme .gt_sourcenote {
#>   font-size: 90%;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #hbyizqonme .gt_left {
#>   text-align: left;
#> }
#> 
#> #hbyizqonme .gt_center {
#>   text-align: center;
#> }
#> 
#> #hbyizqonme .gt_right {
#>   text-align: right;
#>   font-variant-numeric: tabular-nums;
#> }
#> 
#> #hbyizqonme .gt_font_normal {
#>   font-weight: normal;
#> }
#> 
#> #hbyizqonme .gt_font_bold {
#>   font-weight: bold;
#> }
#> 
#> #hbyizqonme .gt_font_italic {
#>   font-style: italic;
#> }
#> 
#> #hbyizqonme .gt_super {
#>   font-size: 65%;
#> }
#> 
#> #hbyizqonme .gt_footnote_marks {
#>   font-style: italic;
#>   font-weight: normal;
#>   font-size: 75%;
#>   vertical-align: 0.4em;
#> }
#> 
#> #hbyizqonme .gt_asterisk {
#>   font-size: 100%;
#>   vertical-align: 0;
#> }
#> 
#> #hbyizqonme .gt_slash_mark {
#>   font-size: 0.7em;
#>   line-height: 0.7em;
#>   vertical-align: 0.15em;
#> }
#> 
#> #hbyizqonme .gt_fraction_numerator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: 0.45em;
#> }
#> 
#> #hbyizqonme .gt_fraction_denominator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: -0.05em;
#> }
#> </style>
#>   <table class="gt_table">
#>   <thead class="gt_header">
#>     <tr>
#>       <th colspan="6" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>JoinCount Spatial Tests (asymptotic)</th>
#>     </tr>
#>     
#>   </thead>
#>   <thead class="gt_col_headings">
#>     <tr>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">pairs</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">z-value</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">pvalue</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Joincount</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Expected</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Variance</th>
#>     </tr>
#>   </thead>
#>   <tbody class="gt_table_body">
#>     <tr class="gt_group_heading_row">
#>       <td colspan="6" class="gt_group_heading">fx - binomial - alternative: greater - Join count test under nonfree sampling</td>
#>     </tr>
#>     <tr class="gt_row_group_first"><td class="gt_row gt_left">high-high</td>
#> <td class="gt_row gt_right">6.33</td>
#> <td class="gt_row gt_right">0.00000</td>
#> <td class="gt_row gt_right">54</td>
#> <td class="gt_row gt_right">27.22</td>
#> <td class="gt_row gt_right">17.89</td></tr>
#>     <tr><td class="gt_row gt_left">low-low</td>
#> <td class="gt_row gt_right">1.01</td>
#> <td class="gt_row gt_right">0.15527</td>
#> <td class="gt_row gt_right">34</td>
#> <td class="gt_row gt_right">29.59</td>
#> <td class="gt_row gt_right">18.90</td></tr>
#>     <tr><td class="gt_row gt_left">high-low</td>
#> <td class="gt_row gt_right">&minus;6.09</td>
#> <td class="gt_row gt_right">1.00000</td>
#> <td class="gt_row gt_right">28</td>
#> <td class="gt_row gt_right">59.18</td>
#> <td class="gt_row gt_right">26.23</td></tr>
#>   </tbody>
#>   
#>   
#> </table>
#> </div>
 jc5 <- jc.test(fx = HICRIME,
                listw = spdep::nb2listw(COL.nb, style="B"),
                distr = "mc")
 summary(jc5)
#> <div id="ojlndidqrg" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
#>   <style>html {
#>   font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
#> }
#> 
#> #ojlndidqrg .gt_table {
#>   display: table;
#>   border-collapse: collapse;
#>   margin-left: auto;
#>   margin-right: auto;
#>   color: #333333;
#>   font-size: 16px;
#>   font-weight: normal;
#>   font-style: normal;
#>   background-color: #FFFFFF;
#>   width: auto;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #A8A8A8;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #A8A8A8;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#> }
#> 
#> #ojlndidqrg .gt_heading {
#>   background-color: #FFFFFF;
#>   text-align: center;
#>   border-bottom-color: #FFFFFF;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #ojlndidqrg .gt_title {
#>   color: #333333;
#>   font-size: 125%;
#>   font-weight: initial;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-color: #FFFFFF;
#>   border-bottom-width: 0;
#> }
#> 
#> #ojlndidqrg .gt_subtitle {
#>   color: #333333;
#>   font-size: 85%;
#>   font-weight: initial;
#>   padding-top: 0;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-color: #FFFFFF;
#>   border-top-width: 0;
#> }
#> 
#> #ojlndidqrg .gt_bottom_border {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #ojlndidqrg .gt_col_headings {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #ojlndidqrg .gt_col_heading {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   overflow-x: hidden;
#> }
#> 
#> #ojlndidqrg .gt_column_spanner_outer {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   padding-top: 0;
#>   padding-bottom: 0;
#>   padding-left: 4px;
#>   padding-right: 4px;
#> }
#> 
#> #ojlndidqrg .gt_column_spanner_outer:first-child {
#>   padding-left: 0;
#> }
#> 
#> #ojlndidqrg .gt_column_spanner_outer:last-child {
#>   padding-right: 0;
#> }
#> 
#> #ojlndidqrg .gt_column_spanner {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 5px;
#>   overflow-x: hidden;
#>   display: inline-block;
#>   width: 100%;
#> }
#> 
#> #ojlndidqrg .gt_group_heading {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #ojlndidqrg .gt_empty_group_heading {
#>   padding: 0.5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #ojlndidqrg .gt_from_md > :first-child {
#>   margin-top: 0;
#> }
#> 
#> #ojlndidqrg .gt_from_md > :last-child {
#>   margin-bottom: 0;
#> }
#> 
#> #ojlndidqrg .gt_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   margin: 10px;
#>   border-top-style: solid;
#>   border-top-width: 1px;
#>   border-top-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#>   overflow-x: hidden;
#> }
#> 
#> #ojlndidqrg .gt_stub {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #ojlndidqrg .gt_stub_row_group {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   vertical-align: top;
#> }
#> 
#> #ojlndidqrg .gt_row_group_first td {
#>   border-top-width: 2px;
#> }
#> 
#> #ojlndidqrg .gt_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #ojlndidqrg .gt_first_summary_row {
#>   border-top-style: solid;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #ojlndidqrg .gt_first_summary_row.thick {
#>   border-top-width: 2px;
#> }
#> 
#> #ojlndidqrg .gt_last_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #ojlndidqrg .gt_grand_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #ojlndidqrg .gt_first_grand_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-style: double;
#>   border-top-width: 6px;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #ojlndidqrg .gt_striped {
#>   background-color: rgba(128, 128, 128, 0.05);
#> }
#> 
#> #ojlndidqrg .gt_table_body {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #ojlndidqrg .gt_footnotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #ojlndidqrg .gt_footnote {
#>   margin: 0px;
#>   font-size: 90%;
#>   padding-left: 4px;
#>   padding-right: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #ojlndidqrg .gt_sourcenotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #ojlndidqrg .gt_sourcenote {
#>   font-size: 90%;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #ojlndidqrg .gt_left {
#>   text-align: left;
#> }
#> 
#> #ojlndidqrg .gt_center {
#>   text-align: center;
#> }
#> 
#> #ojlndidqrg .gt_right {
#>   text-align: right;
#>   font-variant-numeric: tabular-nums;
#> }
#> 
#> #ojlndidqrg .gt_font_normal {
#>   font-weight: normal;
#> }
#> 
#> #ojlndidqrg .gt_font_bold {
#>   font-weight: bold;
#> }
#> 
#> #ojlndidqrg .gt_font_italic {
#>   font-style: italic;
#> }
#> 
#> #ojlndidqrg .gt_super {
#>   font-size: 65%;
#> }
#> 
#> #ojlndidqrg .gt_footnote_marks {
#>   font-style: italic;
#>   font-weight: normal;
#>   font-size: 75%;
#>   vertical-align: 0.4em;
#> }
#> 
#> #ojlndidqrg .gt_asterisk {
#>   font-size: 100%;
#>   vertical-align: 0;
#> }
#> 
#> #ojlndidqrg .gt_slash_mark {
#>   font-size: 0.7em;
#>   line-height: 0.7em;
#>   vertical-align: 0.15em;
#> }
#> 
#> #ojlndidqrg .gt_fraction_numerator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: 0.45em;
#> }
#> 
#> #ojlndidqrg .gt_fraction_denominator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: -0.05em;
#> }
#> </style>
#>   <table class="gt_table">
#>   <thead class="gt_header">
#>     <tr>
#>       <th colspan="5" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>JoinCount Spatial Tests (Monte Carlo)</th>
#>     </tr>
#>     
#>   </thead>
#>   <thead class="gt_col_headings">
#>     <tr>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">pairs</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">pvalue</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Joincount</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Expected</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Variance</th>
#>     </tr>
#>   </thead>
#>   <tbody class="gt_table_body">
#>     <tr class="gt_group_heading_row">
#>       <td colspan="5" class="gt_group_heading">fx - binomial - alternative: greater - Monte-Carlo simulation of join-count statistic</td>
#>     </tr>
#>     <tr class="gt_row_group_first"><td class="gt_row gt_left">high-high</td>
#> <td class="gt_row gt_right">0.00100</td>
#> <td class="gt_row gt_right">54</td>
#> <td class="gt_row gt_right">27.37</td>
#> <td class="gt_row gt_right">18.76</td></tr>
#>     <tr><td class="gt_row gt_left">low-low</td>
#> <td class="gt_row gt_right">0.13600</td>
#> <td class="gt_row gt_right">34</td>
#> <td class="gt_row gt_right">29.38</td>
#> <td class="gt_row gt_right">18.08</td></tr>
#>   </tbody>
#>   
#>   
#> </table>
#> </div>
 HICRIME <- cut(COL.OLD$CRIME, breaks = c(0, 35, 80),
                labels = c("low","high"))
 names(HICRIME) <- rownames(COL.OLD)
 jc6 <- jc.test(fx = HICRIME,
                listw = spdep::nb2listw(COL.nb,
                                 style = "B"))
summary(jc6)
#> <div id="zcgtvsbuev" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
#>   <style>html {
#>   font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
#> }
#> 
#> #zcgtvsbuev .gt_table {
#>   display: table;
#>   border-collapse: collapse;
#>   margin-left: auto;
#>   margin-right: auto;
#>   color: #333333;
#>   font-size: 16px;
#>   font-weight: normal;
#>   font-style: normal;
#>   background-color: #FFFFFF;
#>   width: auto;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #A8A8A8;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #A8A8A8;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#> }
#> 
#> #zcgtvsbuev .gt_heading {
#>   background-color: #FFFFFF;
#>   text-align: center;
#>   border-bottom-color: #FFFFFF;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #zcgtvsbuev .gt_title {
#>   color: #333333;
#>   font-size: 125%;
#>   font-weight: initial;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-color: #FFFFFF;
#>   border-bottom-width: 0;
#> }
#> 
#> #zcgtvsbuev .gt_subtitle {
#>   color: #333333;
#>   font-size: 85%;
#>   font-weight: initial;
#>   padding-top: 0;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-color: #FFFFFF;
#>   border-top-width: 0;
#> }
#> 
#> #zcgtvsbuev .gt_bottom_border {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #zcgtvsbuev .gt_col_headings {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #zcgtvsbuev .gt_col_heading {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 6px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   overflow-x: hidden;
#> }
#> 
#> #zcgtvsbuev .gt_column_spanner_outer {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: normal;
#>   text-transform: inherit;
#>   padding-top: 0;
#>   padding-bottom: 0;
#>   padding-left: 4px;
#>   padding-right: 4px;
#> }
#> 
#> #zcgtvsbuev .gt_column_spanner_outer:first-child {
#>   padding-left: 0;
#> }
#> 
#> #zcgtvsbuev .gt_column_spanner_outer:last-child {
#>   padding-right: 0;
#> }
#> 
#> #zcgtvsbuev .gt_column_spanner {
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: bottom;
#>   padding-top: 5px;
#>   padding-bottom: 5px;
#>   overflow-x: hidden;
#>   display: inline-block;
#>   width: 100%;
#> }
#> 
#> #zcgtvsbuev .gt_group_heading {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #zcgtvsbuev .gt_empty_group_heading {
#>   padding: 0.5px;
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   vertical-align: middle;
#> }
#> 
#> #zcgtvsbuev .gt_from_md > :first-child {
#>   margin-top: 0;
#> }
#> 
#> #zcgtvsbuev .gt_from_md > :last-child {
#>   margin-bottom: 0;
#> }
#> 
#> #zcgtvsbuev .gt_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   margin: 10px;
#>   border-top-style: solid;
#>   border-top-width: 1px;
#>   border-top-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 1px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 1px;
#>   border-right-color: #D3D3D3;
#>   vertical-align: middle;
#>   overflow-x: hidden;
#> }
#> 
#> #zcgtvsbuev .gt_stub {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #zcgtvsbuev .gt_stub_row_group {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   font-size: 100%;
#>   font-weight: initial;
#>   text-transform: inherit;
#>   border-right-style: solid;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   vertical-align: top;
#> }
#> 
#> #zcgtvsbuev .gt_row_group_first td {
#>   border-top-width: 2px;
#> }
#> 
#> #zcgtvsbuev .gt_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #zcgtvsbuev .gt_first_summary_row {
#>   border-top-style: solid;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #zcgtvsbuev .gt_first_summary_row.thick {
#>   border-top-width: 2px;
#> }
#> 
#> #zcgtvsbuev .gt_last_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #zcgtvsbuev .gt_grand_summary_row {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   text-transform: inherit;
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #zcgtvsbuev .gt_first_grand_summary_row {
#>   padding-top: 8px;
#>   padding-bottom: 8px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#>   border-top-style: double;
#>   border-top-width: 6px;
#>   border-top-color: #D3D3D3;
#> }
#> 
#> #zcgtvsbuev .gt_striped {
#>   background-color: rgba(128, 128, 128, 0.05);
#> }
#> 
#> #zcgtvsbuev .gt_table_body {
#>   border-top-style: solid;
#>   border-top-width: 2px;
#>   border-top-color: #D3D3D3;
#>   border-bottom-style: solid;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#> }
#> 
#> #zcgtvsbuev .gt_footnotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #zcgtvsbuev .gt_footnote {
#>   margin: 0px;
#>   font-size: 90%;
#>   padding-left: 4px;
#>   padding-right: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #zcgtvsbuev .gt_sourcenotes {
#>   color: #333333;
#>   background-color: #FFFFFF;
#>   border-bottom-style: none;
#>   border-bottom-width: 2px;
#>   border-bottom-color: #D3D3D3;
#>   border-left-style: none;
#>   border-left-width: 2px;
#>   border-left-color: #D3D3D3;
#>   border-right-style: none;
#>   border-right-width: 2px;
#>   border-right-color: #D3D3D3;
#> }
#> 
#> #zcgtvsbuev .gt_sourcenote {
#>   font-size: 90%;
#>   padding-top: 4px;
#>   padding-bottom: 4px;
#>   padding-left: 5px;
#>   padding-right: 5px;
#> }
#> 
#> #zcgtvsbuev .gt_left {
#>   text-align: left;
#> }
#> 
#> #zcgtvsbuev .gt_center {
#>   text-align: center;
#> }
#> 
#> #zcgtvsbuev .gt_right {
#>   text-align: right;
#>   font-variant-numeric: tabular-nums;
#> }
#> 
#> #zcgtvsbuev .gt_font_normal {
#>   font-weight: normal;
#> }
#> 
#> #zcgtvsbuev .gt_font_bold {
#>   font-weight: bold;
#> }
#> 
#> #zcgtvsbuev .gt_font_italic {
#>   font-style: italic;
#> }
#> 
#> #zcgtvsbuev .gt_super {
#>   font-size: 65%;
#> }
#> 
#> #zcgtvsbuev .gt_footnote_marks {
#>   font-style: italic;
#>   font-weight: normal;
#>   font-size: 75%;
#>   vertical-align: 0.4em;
#> }
#> 
#> #zcgtvsbuev .gt_asterisk {
#>   font-size: 100%;
#>   vertical-align: 0;
#> }
#> 
#> #zcgtvsbuev .gt_slash_mark {
#>   font-size: 0.7em;
#>   line-height: 0.7em;
#>   vertical-align: 0.15em;
#> }
#> 
#> #zcgtvsbuev .gt_fraction_numerator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: 0.45em;
#> }
#> 
#> #zcgtvsbuev .gt_fraction_denominator {
#>   font-size: 0.6em;
#>   line-height: 0.6em;
#>   vertical-align: -0.05em;
#> }
#> </style>
#>   <table class="gt_table">
#>   <thead class="gt_header">
#>     <tr>
#>       <th colspan="6" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>JoinCount Spatial Tests (asymptotic)</th>
#>     </tr>
#>     
#>   </thead>
#>   <thead class="gt_col_headings">
#>     <tr>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">pairs</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">z-value</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">pvalue</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Joincount</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Expected</th>
#>       <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">Variance</th>
#>     </tr>
#>   </thead>
#>   <tbody class="gt_table_body">
#>     <tr class="gt_group_heading_row">
#>       <td colspan="6" class="gt_group_heading">fx - binomial - alternative: greater - Join count test under nonfree sampling</td>
#>     </tr>
#>     <tr class="gt_row_group_first"><td class="gt_row gt_left">high-high</td>
#> <td class="gt_row gt_right">6.33</td>
#> <td class="gt_row gt_right">0.00000</td>
#> <td class="gt_row gt_right">54</td>
#> <td class="gt_row gt_right">27.22</td>
#> <td class="gt_row gt_right">17.89</td></tr>
#>     <tr><td class="gt_row gt_left">low-low</td>
#> <td class="gt_row gt_right">1.01</td>
#> <td class="gt_row gt_right">0.15527</td>
#> <td class="gt_row gt_right">34</td>
#> <td class="gt_row gt_right">29.59</td>
#> <td class="gt_row gt_right">18.90</td></tr>
#>     <tr><td class="gt_row gt_left">high-low</td>
#> <td class="gt_row gt_right">&minus;6.09</td>
#> <td class="gt_row gt_right">1.00000</td>
#> <td class="gt_row gt_right">28</td>
#> <td class="gt_row gt_right">59.18</td>
#> <td class="gt_row gt_right">26.23</td></tr>
#>   </tbody>
#>   
#>   
#> </table>
#> </div>