# Compute the QE and QI tests of Equivalence and Independence between maps This function compute the QE and QI tests for maps comparison based on symbolic entropy. ```r Q.map.test(formula = formula, data = data, coor = NULL, m = m, r = 1, type = "combinations", control = list()) ``` ## Arguments - `formula`: a symbolic description of the two factors. - `data`: (optional) a data frame or a sf object containing the variables to testing for. - `coor`: (optional) a 2xN vector with coordinates. - `m`: length of m-surrounding. - `r`: maximum overlapping between any two m-surroundings (default = 1). - `type`: Type of symbols: "permutations" or "combinations". Default "combinations" - `control`: Optional argument. See Control Argument section. ## Returns A list with two objects of the class `htest`. The first one is the QE test of Equivalence between maps and the second one is the QI test of independence between maps. the elements of each test are: ||| |:--|:--| |`method`|a character string giving description of the method.| |`data.name`|a character string giving the name(s) of the data.| |`statistic`|the value of the statistic QE or/and QI.| |`alternative`|a character string describing the alternative hypothesis.| |`p.value`|p-value for QE or QI.| |`parameter`|free degree of the statistic for QE or QI.| |`symb`|A matrix with the symbols.| |`mh`|m-surrounding of th map.| |`Tm`|number of maps (ONLY 2).| |`sample.size`|number of symbolized observations.| |`nsk`|a matrix Tm x symbols with the frequency of the number of symbols of each map.| ## Details If `data` is not a sf object the `coor` argument with the coordinates of each observation must be included. ## Control arguments Several parameters to construct the m-surrounding - **dtmaxabs**: Delete degenerate surrounding based on the absolute distance between observations. - **dtmaxpc**: A value between 0 and 1. Delete degenerate surrounding based on the distance. Delete m-surrounding when the maximum distance between observation is upper than k percentage of maximum distance between anywhere observation. - **dtmaxknn**: A integer value 'k'. Delete degenerate surrounding based on the near neighborhood criteria. Delete m-surrounding is a element of the m-surrounding is not include in the set of k near neighborhood of the first element - **seedinit**: seed to select the initial element to star the algorithm to compute the m-surroundings. ## Examples ```r # Case 1: N <- 200 cx <- runif(N) cy <- runif(N) x <- cbind(cx,cy) listw <- spdep::nb2listw(spdep::knn2nb( spdep::knearneigh(cbind(cx,cy), k = 4))) p <- c(1/6, 3/6, 2/6) rho = 0.5 QY1 <- dgp.spq(p = p, listw = listw, rho = rho) rho = 0.8 QY2 <- dgp.spq(p = p, listw = listw, rho = rho) dt = data.frame(QY1,QY2) m = 3 r = 1 formula <- ~ QY1 + QY2 control <- list(dtmaxknn = 10) qmap <- Q.map.test(formula = formula, data = dt, coor = x, m = m, r = r, type ="combinations", control = control) print(qmap) plot(qmap) plot(qmap, ci=.6) plot(qmap[[1]]$mh) summary(qmap[[1]]$mh) control <- list(dtmaxknn = 20) qmap <- Q.map.test(formula = formula, data = dt, coor = x, m = m, r = r, type ="permutations", control = control) print(qmap) plot(qmap) plot(qmap[[1]]$mh) qmap <- Q.map.test(formula = formula, data = dt, coor = x, m = m, r = r, type ="combinations") print(qmap) plot(qmap) control <- list(dtmaxknn = 10) qmap <- Q.map.test(formula = formula, data = dt, coor = x, m = m, r = r, type ="combinations", control = control) print(qmap) plot(qmap) # Case 2: data(provinces_spain) # sf::sf_use_s2(FALSE) m = 3 r = 1 provinces_spain$Mal2Fml <- factor(provinces_spain$Mal2Fml > 100) levels(provinces_spain$Mal2Fml) = c("men","woman") provinces_spain$Coast <- factor(provinces_spain$Coast) levels(provinces_spain$Coast) = c("no","yes") formula <- ~ Coast + Mal2Fml qmap <- Q.map.test(formula = formula, data = provinces_spain, m = m, r = r, type ="combinations") print(qmap) plot(qmap) plot(qmap[[1]]$mh) control <- list(dtmaxknn = 6) qmap <- Q.map.test(formula = formula, data = provinces_spain, m = m, r = r, type ="combinations", control = control) print(qmap) plot(qmap[[1]]$mh) summary(qmap[[1]]$mh) ``` ## References * Ruiz M, López FA and A Páez (2011). Comparison of Thematic Maps Using Symbolic Entropy. **International Journal of Geographical Information Science**, 26, 413-439. * Ruiz, M., López, FA, and Páez, A. (2010). Testing for spatial association of qualitative data using symbolic dynamics. **Journal of Geographical Systems**, 12(3), 281-309.0. ## See Also `dgp.spq`, `m.surround`, `Q.test` ## Author(s) ||| |:--|:--| |Fernando López|fernando.lopez@upct.es| |Román Mínguez|roman.minguez@uclm.es| |Antonio Páez|paezha@gmail.com| |Manuel Ruiz|manuel.ruiz@upct.es|

Q.map.test function