Univariate and multivariable local spatial analysis. This program computes Getis-Ord G and G*, and LISA's (local Moran and local Geary) statistics for the data Z, with P-values or bootstrap confidence intervals.
eco.lsa(var, con, method = c("G*", "G", "I", "C"), zerocon = NA, nsim = 99, conditional = c("auto", "TRUE", "FALSE"), test = c("permutation", "bootstrap"), alternative = c("auto", "two.sided", "greater", "less"), adjust = "none", multi = c("matrix", "list"), pop = NULL)
| var | Vector, matrix or data frame for the analysis. Multiple variables in columns. |
|---|---|
| con | An object of class eco.weight obtained with the function |
| method | Method of analysis: "G" for Getis-Ord G, "G*" for Getis-Ord G*, "I" for local Moran's I or "C" for local Geary's C. |
| zerocon | If zerocon = 0 the program assigns the value 0 to those individuals with no connections; if zerocon = NA the program assigns NA. Default is NA. |
| nsim | Number of Monte-Carlo simulations. |
| conditional | Logical. Should be used a conditional randomization? (Anselin 1998, Sokal and Thomson 2006). The option "auto" sets conditional = TRUE for LISA methods and G, as suggested by Sokal (2008). |
| test | If test = "bootstrap", for each individual test, the program generates a bootstrap resampling and the associated confidence intervals of the null hypotesis. If test = "permutation" (default) a permutation test is made and the P-value is computed. |
| alternative | The alternative hypothesis for "permutation" test. If "auto" is selected (default) the program determines the alternative hypothesis in each individual test. Other options are: "two.sided", "greater" and "less". |
| adjust | Correction method of P-values for multiple tests,
passed to |
| multi | multiple output format results. "list" for object with a list of individual test for each variable, or "matrix" for results as matrices of multiples variables. |
| pop | numeric factor with the population of each individual. Optional for multiple tests with multi = "matrix". |
For single test, the program returns an object of class "eco.lsa" with the following slots:
> OUT results - table with output results.
--> If test = "permutation": observed value of the statistic , null confidence interval and #rescaled observed value to [-1, 1] range, as in Sokal (2006)
--> If test = "bootstrap": observed and expected value of the statistic, alternative hypotesis, null confidence interval and rescaled observed value to [-1, 1] range, as in Sokal (2006)
> METHOD method (coefficent) used in the analysis
> TEST test method used (bootstrap, permutation)
> NSIM number of simulations
> PADJUST P-values adjust method for permutation tests
> COND conditional randomization (logical)
> XY input coordinates
For multiple test, if the parameter multi = "list", the program returns a list of eco.lsa objects (one element for each variable).
For multiple test, if the parameter multi = "matrix", the program returns an object of class "eco.multilsa" with the following slots:
> METHOD method used in the analysis
> TEST test method used (bootstrap, permutation)
> NSIM number of simulations
> PADJUST P-values adjust method for permutation tests
> COND conditional randomization (logical)
> XY input coordinates
> OBS observed value
> EXP expected value
> ALTER test alternative
> PVAL pvalue for permutation test
> LWR lower confidence interval bound of the null hypotesis
> UPPR upper confidence interval bound of the null hypotesis
> OBS.RES rescaled observed value to [-1, 1] range, as in Sokal (2006) ACCESS TO THE SLOTS The content of the slots can be accessed with the corresponding accessors, using the generic notation of EcoGenetics (<ecoslot.> + <name of the slot> + <name of the object>). See help("EcoGenetics accessors") and the Examples section below
Anselin L. 1995. Local indicators of spatial association-LISA. Geographical analysis. 27: 93-115.
Getis A., and J. Ord. 1992. The analysis of spatial association by use of distance statistics. Geographical analysis, 24: 189-206.
Ord J., and A. Getis. 1995. Local spatial autocorrelation statistics: distributional issues and an application. Geographical analysis, 27: 286-306.
Sokal R., N. Oden and B. Thomson. 1998. Local spatial autocorrelation in a biological model. Geographical Analysis, 30: 331-354.
Sokal R. and B. Thomson. 2006. Population structure inferred by local spatial autocorrelation: an example from an Amerindian tribal population. American journal of physical anthropology, 129: 121-131.
# NOT RUN { data(eco.test) #---------------------------------------------------------------------------# ##################### # LOCAL MORAN'S I ##################### DETAILED EXAMPLE #------------------------- # TESTING PHENOTYPIC DATA- #------------------------- set.seed(10) # test for a single variable--------------------------------- #computing weights con <- eco.weight(eco[["XY"]], method = "knearest", k = 4, row.sd = TRUE) # row standardized weights = TRUE # test for the first trait of the data frame P localmoran <- eco.lsa(eco[["P"]][, 1], con, method = "I", nsim = 99) # "rankplot" graph eco.plotLocal(localmoran) # test for several variables--------------------------------- # ordering the factor "pop" in increasing order and the object "eco" # in relation to this ordered factor prior to the multivariate analysis. # This step is important for "localplot" graphs. eco <- eco[order(eco[["S"]][,1])] #computing weights with the ordered object con <- eco.weight(eco[["XY"]], method = "knearest", k = 4, row.sd = TRUE) # row standardized weights = TRUE all.traits <- eco.lsa(eco[["P"]], con, method = "I", nsim = 99) # Plot of the phenotypic spatial patterns # "rasterplot" graph eco.plotLocal(all.traits) # in grey: non significant results (P > 0.05) # set significant = FALSE for showing significant and no significant results eco.plotLocal(all.traits, significant = FALSE) # single plots using "rankplot" graphs all.single.traits <- eco.lsa(eco[["P"]],con, method = "I", nsim = 99, multi="list") eco.plotLocal(all.single.traits) # removing legends for a better visualization eco.plotLocal(all.single.traits, legend = FALSE) # - individual plots support ggplot2 sintax (plot equivalent to the previous): eco.plotLocal(all.single.traits) + ggplot2::theme(legend.position="none") #------------------------- # TESTING GENOTYPIC DATA- #------------------------- # eco[["A"]] is a matrix with the genetic data of "eco" # as frequencies for each allele in each individual. head(eco[["A"]]) # head of the matrix - 40 alleles # ordering the factor "pop" in increasing order and the object "eco" # in relation to this ordered factor prior to the multivariate analysis. # This step is important for "localplot" graphs data(eco.test) # for security this resets the data (unordered) eco <- eco[order(eco[["S"]][,1])] # ordering # computing weights with the ordered object con <- eco.weight(eco[["XY"]], method = "knearest", k = 4, row.sd = TRUE) # row standardized weights = TRUE # test for a single allele localmoran.geno <- eco.lsa(eco[["A"]][, 32], con, method = "I", nsim = 99) # test for several alleles - 40 alleles (it runs in less than 1 min # for 99 simulations per allele; 999 simulations takes ~ 11 s per allele, # less than 8 min in total.) all.alleles <- eco.lsa(eco[["A"]], con, method = "I", nsim = 99) # plot all alleles to get an overview of the spatial patterns eco.plotLocal(all.alleles) # in grey: non significant results (P > 0.05) # set significant = FALSE for showing significant and no significant results eco.plotLocal(all.alleles, significant = FALSE) # counting individuals with P < 0.05 for each allele (5 * 225 /100 ~ 12 significant tests # by random) signif <- apply(ecoslot.PVAL(all.alleles), 2, function(x) sum (x < 0.05)) # filtering alleles, loci with > 12 significant individual tests A.local <- eco[["A"]][, signif > 12] #filtered matrix all.alleles.f <- eco.lsa(eco[["A"]][, signif > 12] , con, method = "I", nsim = 99) # Plot of the genotypic spatial patterns using "localplot" graphs eco.plotLocal(all.alleles.f) ## using "rankplot" graphs all.sf <- eco.lsa(A.local, 2, eco.lsa, con, method = "I", nsim = 99, multi = "list") eco.plotLocal(all.sf, legend = FALSE) ##################### # GETIS-ORD'S G* ##################### con<- eco.weight(eco[["XY"]], method = "knearest", k = 4, self = TRUE) # self = TRUE for G* getis.ak <- eco.lsa(eco[["P"]][, 1], con, method = "G*", nsim = 99, adjust = "none") getis.ak ### to plot the results, the function "eco.lsa" calls "eco.rankplot" ### (see ?eco.rankplot) when test = "permutation" and "eco.forestplot" (see ?eco.forestplot) ### when test = "bootstrap" p <- eco.plotLocal(getis.ak) # rankplot graph p # points with colors of the color-scale: # points with P < 0.05. Yellow points : points with P > 0.05 p <- eco.plotLocal(getis.ak, significant = FALSE) p # all points have a color of the color-scale #----------------------- # ACCESSORS USE EXAMPLE #----------------------- # the slots are accessed with the generic format # (ecoslot. + name of the slot + name of the object). # See help("EcoGenetics accessors") ecoslot.OUT(getis.ak) ## bootstrap example getis.akb <- eco.lsa(eco[["P"]][, 1], con, method = "G*", nsim = 99, test = "bootstrap") p <- eco.plotLocal(getis.akb) # forestplot graph p2 <- eco.plotLocal(getis.akb, interactivePlot = FALSE) p2 + ggplot2::theme_bw() # the plot can be modified with ggplot2 # In this case, the background is modified (white color) #---------------------------------------------------------------------------# ##################### # GETIS-ORD'S G ##################### con <- eco.weight(eco[["XY"]], method = "knearest", k = 4) # self = FALSE for G getis <- eco.lsa(eco[["P"]][, 1], con, method = "G", nsim = 99) eco.plotLocal(getis) #---------------------------------------------------------------------------# ##################### # LOCAL GEARY'S C ##################### con<- eco.weight(eco[["XY"]], method = "knearest", k = 4, row.sd = TRUE) # row standardized weights = TRUE localgeary <- eco.lsa(eco[["P"]][, 1], con, method = "C", nsim = 99, adjust = "none") eco.plotLocal(localgeary) # }