CDOoDocuments.StdDocumentDescDocuments.DocumentDescContainers.ViewDescViews.ViewDescStores.StoreDescBDocuments.ModelDescContainers.ModelDescModels.ModelDescStores.ElemDesciA aATextViews.StdViewDescTextViews.ViewDesc ATextModels.StdModelDescTextModels.ModelDesc??&TextModels.AttributesDesc'*= '*Ȝ '*PS 6*PSFv *PS3k + - `y*uTTextRulers.StdRulerDescTextRulers.RulerDescTextRulers.StdStyleDescTextRulers.StyleDescTextRulers.AttributesDesc\ Zo@w#$.@::A`Ey 6*PSȜ B*PS,k *uTY?$ Zo9  ?SymbolPSI +P 9w '* '* +ArialPS 5ArialPSB c +Arial ArialPS'  1    85 =S   ' xStdFolds.FoldDesc  y: Arial5click on one of the arrows to open the initial values  ZArialPS  "   x   +Arial 5Arial  2Arial. r '* * 27      l4 list( N_LOC=476, N_nonzeroy=351, 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num=c(3,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,3,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,3,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,3), 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,194,196,211,212,213,178,179,180,195,197,212,213,214,179,180,181,196,198,213,214,215,180,181,182,197,199,214,215,216,181,182,183,198,200,215,216,217,182,183,184,199,201,216,217,218,183,184,185,200,202,217,218,219,184,185,186,201,203,218,219,220,185,186,187,202,204,219,220,221,186,187,203,220,221,188,189,206,222,223,188,189,190,205,207,222,223,224,189,190,191,206,208,223,224,225,190,191,192,207,209,224,225,226,191,192,193,208,210,225,226,227,192,193,194,209,211,226,227,228,193,194,195,210,212,227,228,229,194,195,196,211,213,228,229,230,195,196,197,212,214,229,230,231,196,197,198,213,215,230,231,232,197,198,199,214,216,231,232,233,198,199,200,215,217,232,233,234,199,200,201,216,218,233,234,235,200,201,202,217,219,234,235,236,201,202,203,218,220,235,236,237,202,203,204,219,221,236,237,238,203,204,220,237,238,205,206,223,239,240,205,206,207,222,224,239,240,241,206,207,208,223,225,240,241,242,207,208,209,224,226,241,242,243,208,209,210,225,227,242,243,244,209,210,211,226,228,243,244,245,210,211,212,227,229,244,245,246,211,212,213,228,230,245,246,247,212,213,214,229,231,246,247,248,213,214,215,230,232,247,248,249,214,215,216,231,233,248,249,250,215,216,217,232,234,249,250,251,216,217,218,233,235,250,251,252,217,218,219,234,236,251,252,253,218,219,220,235,237,252,253,254,219,220,221,236,238,253,254,255,220,221,237,254,255,222,223,240,256,257,222,223,224,239,241,256,257,258,223,224,225,240,242,257,258,259,224,225,226,241,243,258,259,260,225,226,227,242,244,259,260,261,226,227,228,243,245,260,261,262,227,228,229,244,246,261,262,263,228,229,230,245,247,262,263,264,229,230,231,246,248,263,264,265,230,231,232,247,249,264,265,266,231,232,233,248,250,265,266,267,232,233,234,249,251,266,267,268,233,234,235,250,252,267,268,269,234,235,236,251,253,268,269,270,235,236,237,252,254,269,270,271,236,237,238,253,255,270,271,272,237,238,254,271,272,239,240,257,273,274,239,240,241,256,258,273,274,275,240,241,242,257,259,274,275,276,241,242,243,258,260,275,276,277,242,243,244,259,261,276,277,278,243,244,245,260,262,277,278,279,244,245,246,261,263,278,279,280,245,246,247,262,264,279,280,281,246,247,248,263,265,280,281,282,247,248,249,264,266,281,282,283,248,249,250,265,267,282,283,284,249,250,251,266,268,283,284,285,250,251,252,267,269,284,285,286,251,252,253,268,270,285,286,287,252,253,254,269,271,286,287,288,253,254,255,270,272,287,288,289,254,255,271,288,289,256,257,274,290,291,256,257,258,273,275,290,291,292,257,258,259,274,276,291,292,293,258,259,260,275,277,292,293,294,259,260,261,276,278,293,294,295,260,261,262,277,279,294,295,296,261,262,263,278,280,295,296,297,262,263,264,279,281,296,297,298,263,264,265,280,282,297,298,299,264,265,266,281,283,298,299,300,265,266,267,282,284,299,300,301,266,267,268,283,285,300,301,302,267,268,269,284,286,301,302,303,268,269,270,285,287,302,303,304,269,270,271,286,288,303,304,305,270,271,272,287,289,304,305,306,271,272,288,305,306,273,274,291,307,308,273,274,275,290,292,307,308,309,274,275,276,291,293,308,309,310,275,276,277,292,294,309,310,311,276,277,278,293,295,310,311,312,277,278,279,294,296,311,312,313,278,279,280,295,297,312,313,314,279,280,281,296,298,313,314,315,280,281,282,297,299,314,315,316,281,282,283,298,300,315,316,317,282,283,284,299,301,316,317,318,283,284,285,300,302,317,318,319,284,285,286,301,303,318,319,320,285,286,287,302,304,319,320,321,286,287,288,303,305,320,321,322,287,288,289,304,306,321,322,323,288,289,305,322,323,290,291,308,324,325,290,291,292,307,309,324,325,326,291,292,293,308,310,325,326,327,292,293,294,309,311,326,327,328,293,294,295,310,312,327,328,329,294,295,296,311,313,328,329,330,295,296,297,312,314,329,330,331,296,297,298,313,315,330,331,332,297,298,299,314,316,331,332,333,298,299,300,315,317,332,333,334,299,300,301,316,318,333,334,335,300,301,302,317,319,334,335,336,301,302,303,318,320,335,336,337,302,303,304,319,321,336,337,338,303,304,305,320,322,337,338,339,304,305,306,321,323,338,339,340,305,306,322,339,340,307,308,325,341,342,307,308,309,324,326,341,342,343,308,309,310,325,327,342,343,344,309,310,311,326,328,343,344,345,310,311,312,327,329,344,345,346,311,312,313,328,330,345,346,347,312,313,314,329,331,346,347,348,313,314,315,330,332,347,348,349,314,315,316,331,333,348,349,350,315,316,317,332,334,349,350,351,316,317,318,333,335,350,351,352,317,318,319,334,336,351,352,353,318,319,320,335,337,352,353,354,319,320,321,336,338,353,354,355,320,321,322,337,339,354,355,356,321,322,323,338,340,355,356,357,322,323,339,356,357,324,325,342,358,359,324,325,326,341,343,358,359,360,325,326,327,342,344,359,360,361,326,327,328,343,345,360,361,362,327,328,329,344,346,361,362,363,328,329,330,345,347,362,363,364,329,330,331,346,348,363,364,365,330,331,332,347,349,364,365,366,331,332,333,348,350,365,366,367,332,333,334,349,351,366,367,368,333,334,335,350,352,367,368,369,334,335,336,351,353,368,369,370,335,336,337,352,354,369,370,371,336,337,338,353,355,370,371,372,337,338,339,354,356,371,372,373,338,339,340,355,357,372,373,374,339,340,356,373,374,341,342,359,375,376,341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sumNumNeigh=3542)-.?   .y _ A '* * 27      l4 list( N_LOC=476, N_nonzeroy=351, 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sumNumNeigh=3542)-. WinBUGS Lab Exercise 4 Nov. 2004 Andrew Latimer & Shanshan Wu The code included here implements a simple GLM, and a spatially explicit regression model. For the purpose of these examples, we include data for a small region including 476 one minute by one minute grid cells. This region is is a small corner of South Africa's Cape Floristic Region, and includes very high plant species diversity and a World Biosphere Reserve (see http://www.capenature.org.za/Nature_Reserves/html/kogelberg.html). The data sets include (see Table 1): 1) n[i] = the number of sample locations in each cell (which can be zero); 2) y[i] = the number of times the species was observed to be present in each cell -- this is provided for two plant species, Protea cynaroides (common, the national flower of South Africa) and Mimetes arboreus (rare, Red Data List species); 3) a set of 6 environmental covariates: Elevational range or "roughness" (rough[i]), July minimum temperature (julmint[i]), interannual variation in precipitation (pptcv[i]), summer soil moisture days (smdsum[i]), enhanced vegetation or "greenness" index (evi[i]), and percent acidic soil (ph1[i]); and 4) adj[] = the spatial position of each grid cell, expressed as a list of adjacent cells. Together with num[i] = number of neighbors of each cell, this is a sparse representation of the adjacency matrix for the subregion. Table 1: Sample Data Format.  Pixel Number Number of Covariates Adjacent of visits presence cells ni yi x1i ... x6i _________________________________________________________________ 1 7 0 0.227696 ... -0.350282 2,6,7 2 7 0 0.227696 ... -0.441250 1,3,6,7,8 ... ... ... ... ... ... ... 476 8 0 0.442076 ... -0.250218 151,152,153,160  The non-spatial model, Model 1, can be written as: For ni >0, yi ~ Bin(ni , pi) logit pi = mu + x1ib1 + x2ib2 +x3ib3 +x4ib4 Note that for n_i =0, there is no contribution of grid cell i to the likelihood. Accordingly, the code includes an index vector, ind[], to hold the row numbers of the sampled cells, and an integer variable, N_nonzeroy, that stores the number of sampled cells. The spatial model, Model 2, adds a set of spatial random effects (Rho[i]): For ni >0, yi ~ Bin(ni , pi) logit pi = mu + Rhoi + x1ib1 + x2ib2 +x3ib3 +x4ib4 We assume a CAR prior for rho. Note that for unvisited sites, the inference for rho_i is entirely by "borrow strength" from its neighbors. Suggestions on running the models and displaying results Suggested run duration: 5,000+ samples for burn-in, 10,000+ samples for inference. Note the model runs MUCH more slowly when it is calculating DIC, so I'd do that only for a portion of the run. Check autocorrelation of the regression coefficients in the non-spatial versus spatial model, then thin by some amount to reduce autocorrelation. Compare the coefficient estimates (beta) for the two models. To view a 2-d map display of the p[i]'s after running a model: 1) In Sample Monitor Tool, click on the stats button for node p, delete the header row, and save as a text (.txt) file. 2) Do the same for node rho (the spatial random effects). 2) Run R and use File>Change dir... to set your working directory to the file where you saved the model output files. 3) From my website, http://www.eeb.uconn.edu/grads/latimer/Downloads, open the text file "Gelfandlabdata.txt" and Copy and Paste the entire contents to the R command line. 4) From the same place, open the text file "Gelfand2dplot.txt", type in the name of the text file for p at the appropriate place, then Copy and Paste the entire contents of the file to the R command line. WinBUGS Code for Model 1: Model { # likelihood for (i in 1 : N_nonzeroy) { y[ind[i]] ~ dbin(p[ind[i]], n[ind[i]]) } for(i in 1:N_LOC){ logit(p[i]) <- xbeta[i]+mu xbeta[i]<-beta[1]*rough[i] + beta[2]*julmint[i] + beta[3]*pptcv[i] + beta[4]*smdsum[i] + beta[5]*evi[i] + beta[6]*ph1[i] } temp<-adj[1]+sumNumNeigh+num[1] # priors mu ~ dnorm(0,0.1) for ( i in 1:6) { beta[i] ~ dnorm(0, 0.2) } } Data Use the data for either species below. Model 1 Inits list(mu=1, beta=c(1.5, 1.5, 1.5, 1.5, 1.5, 1.5)) WinBUGS Code for Model 2: Model { # likelihood for (i in 1 : N_nonzeroy) { y[ind[i]] ~ dbin(p[ind[i]], n[ind[i]]) } for(i in 1:N_LOC){ logit(p[i]) <- rho[i]+xbeta[i]+mu xbeta[i]<-beta[1]*rough[i] + beta[2]*julmint[i] + beta[3]*pptcv[i] + beta[4]*smdsum[i] + beta[5]*evi[i] + beta[6]*ph1[i] } # CAR prior distribution for spatial random effects: rho[1:N_LOC] ~ car.normal(adj[], weights[], num[], tau) for(k in 1:sumNumNeigh) { weights[k] <- 1 } # other priors mu ~ dnorm(0,0.1) for ( i in 1:6) { beta[i] ~ dnorm(0, 0.2) } vrho ~ dnorm(0, 0.2) I(0,) tau <- 1/vrho } Data Use the data for either species below. Model 2 Initslist(mu=1, beta=c(1.5, 1.5, 1.5, 1.5, 1.5, 1.5), rho=c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0), vrho=0.1) Data for Models 1 and 2 for Protea cynaroides, a common species: Data  click on one of the arrows to open the data  Data for Models 1 and 2 for Mimetes arboreus, a rare species: Data  click on one of the arrows to open the data  TextControllers.StdCtrlDescTextControllers.ControllerDescContainers.ControllerDescControllers.ControllerDesc aY?$0ZGo * <[ @Documents.ControllerDesc zv ~pk