# ------------------------------------------------
# Atlantic cod habitat --- Areal unit modelling of habitat
# Uses carstm and aegis to develop models and predict
# ------------------------------------------------
# load data common environment and parameter setting
# source( system.file( "scripts", "00_cod_comparisons_data_environment.R", package = "carstm") )
# --------------------------------
# construct basic parameter list defining the main characteristics of the study
# and some plotting parameters (bounding box, projection, bathymetry layout, coastline)
# NOTE: the data selection is the same as in (01_cod_comparisons_basic_stranal.R)
require(carstm)
require(aegis.polygons)
p =list(
speciesname = "Atlantic_cod",
groundfish_species_code = 10, # 10= cod
yrs = 1970:2017,
trawlable_units = "towdistance" # <<<<<<<<<<<<<<<<<<
# trawlable_units = "standardtow"
# trawlable_units = "sweptarea"
)
# --------------------------------
# parameter setting used to filter data via 'survey_db( DS="filter")'
# unlike stratanl, we do not need to remove strata until the last /aggregation step
p = aegis.survey::survey_parameters(
p=p,
selection=list(
biologicals=list(
spec_bio = bio.taxonomy::taxonomy.recode( from="spec", to="parsimonious", tolookup=p$groundfish_species_code )
),
survey=list(
data.source="groundfish",
yr = p$yrs, # time frame for comparison specified above
months=6:8, # "summer"
# dyear = c(150,250)/365, # alternate way of specifying season: summer = which( (x>150) & (x<250) ) , spring = which( x<149 ), winter = which( x>251 )
settype = 1, # same as geartype in groundfish_survey_db
gear = c("Western IIA trawl", "Yankee #36 otter trawl"),
polygon_enforce=TRUE, # make sure mis-classified stations or incorrectly entered positions get filtered out
ranged_data = c("dyear") # not used .. just to show how to use range_data
)
)
)
# ------------------------------------------------
## using the "standard" polygon definitions .. see https://cran.r-project.org/web/packages/spdep/vignettes/nb.pdf
# Here we compute surface area of each polygon via projection to utm or some other appropriate planar projection.
# This adds some variabilty relative to "statanal" (which uses sa in sq nautical miles, btw)
sppoly = areal_units(
areal_units_type="stratanal_polygons_pre2014",
areal_units_proj4string_planar_km=p$areal_units_proj4string_planar_km
)
sppoly$strata_to_keep = ifelse( as.character(sppoly$AUID) %in% strata_definitions( c("Gulf", "Georges_Bank", "Spring", "Deep_Water") ), FALSE, TRUE )
# ------------------------------------------------
# neighbourhood structure --- required to do areal unit spatial modelling
sppoly = neighbourhood_structure( sppoly=sppoly, areal_units_type="stratanal_polygons_pre2014" )
# --------------------------------
# Get the data
p$selection$survey$strata_toremove = NULL # emphasize that all data enters analysis initially ..
set = survey_db( p=p, DS="filter" )
# categorize Strata
crs_lonlat = st_crs(projection_proj4string("lonlat_wgs84"))
sppoly = st_transform(sppoly, crs=crs_lonlat )
set$AUID = st_points_in_polygons(
pts = st_as_sf( set, coords=c("lon","lat"), crs=crs_lonlat ),
polys = sppoly[, "AUID"],
varname="AUID"
)
set = set[ which(!is.na(set$AUID)),]
set$totno[which(!is.finite(set$totno))] = NA
# --------------------------------
# ensure we have some estimate of sweptarea and choose the appropriate
# one based upon which trawlable units we are using
ft2m = 0.3048
m2km = 1/1000
nmi2mi = 1.1507794
mi2ft = 5280
standardtow_sakm2 = (41 * ft2m * m2km ) * ( 1.75 * nmi2mi * mi2ft * ft2m * m2km ) # surface area sampled by a standard tow in km^2 1.75 nm
set$data_offset = switch( p$trawlable_units,
standardtow = rep(standardtow_sakm2, nrow(set)) , # "standard tow"
towdistance = set$sa_towdistance, # "sa"=computed from tow distance and standard width, 0.011801==),
sweptarea = set$sa # swept area based upon stand tow width and variable lenths based upon start-end locations wherever possible
)
set$data_offset[which(!is.finite(set$data_offset))] = median(set$data_offset, na.rm=TRUE ) # just in case missing data
# ------------------------------------------------
# update set with AUID factor variables and a few other repeatedly used variables
# set$AUID = factor(set$AUID, levels=levels(sppoly$AUID))
space.id = slot( sppoly, "space.id" )
set$space = set$space_time = match( set$AUID, space.id )
set$yr_factor = factor(set$yr)
set$time = set$time_space = as.numeric( set$yr_factor)
set$iid_error = 1:nrow(set) # for inla indexing
set$tag = "observations"
## --------------------------------
# construct meanweights matrix
weight_year = meanweights_by_arealunit( set=set, AUID=as.character( sppoly$AUID ), yrs=p$yrs, fillall=TRUE, annual_breakdown=TRUE )
# weight_year = meanweights_by_arealunit_modelled( p=p, redo=TRUE ) -- note: data passing of M needs to be modularized
# weight_year = weight_year[, match(as.character(p$yrs), colnames(weight_year) )]
# weight_year = weight_year[ match(as.character(sppoly$AUID), rownames(weight_year) )]
# RES = data.frame(yr=p$selection$survey[["yr"]]) # collect model comparisons
if (0) {
fn = file.path( project.datadirectory( "carstm" ), "RES.rdata" )
# save(RES, file=fn)
# load(fn)
}
## ----------------------------------
# covariate estimates for prediction in strata and year
covars = c("t", "tsd", "tmax", "tmin", "degreedays", "z", "dZ", "ddZ" )
# currently supported:
# z = depth (m)
# dZ = bottom slope (m/km)
# ddZ = bottom curvature (m/km^2)
# substrate.grainsize = mean grain size of bottom substrate (mm)
# t = temperature (C) – subannual
# tlb = temperature lower 95% bound (C) –subannual
# tub = temperature upper 95% bound (C) –subannual
# tmean = mean annual temperature
# tsd = standard deviation of the mean annual temperature
# tmin = minimum value of temperature in a given year – annual
# tmax= maximum value of temperature in a given year – annual
# tamplitude = amplitude of temperature swings in a year (tmax-tmin) – annual
# degreedays = number of degree days in a given year – annual
res = aegis_db_extract_by_polygon(
sppoly=sppoly,
vars=covars,
spatial_domain=p$spatial_domain,
yrs=p$yrs,
dyear=0.6 # 0.6*12 months = 7.2 = early July
)
# extract covariates and supplent survey data via lookups
set = aegis_db_lookup(
X=set,
lookupvars=covars,
xy_vars=c("lon", "lat"),
time_var="timestamp"
)
pa = presence.absence( X={set$totno / set$data_offset}, px=0.05 ) # determine presence absence and weighting
set[, "pa"] = pa$pa
set[, "wt"] = pa$probs
pa = NULL
# ------------------------------------------------
# good data
ok = which(
is.finite(set$totno) & # INLA can impute Y-data
is.finite(set$t) &
is.finite(set$z) &
is.finite(set$data_offset) &
set$AUID %in% sppoly$AUID[sppoly$strata_to_keep]
)
# ---------------------
# generic PC priors
H = inla_hyperparameters( sd(set$pa) )
# ------------------------------------------------
# Model 1: a binomial (presence-absence) aks, habitat probability model with linear covariate effects
fit = glm(
formula = pa ~ 1 + t + z +degreedays,
family=binomial(link="logit"),
data=set
)
if (0) {
fnx = file.path( project.datadirectory( "carstm" ), "fit_habitat_glm.rdata" )
save( fit, file=fnx )
# load(fnx)
}
s = summary(fit)
AIC(fit) # 10774
toplot = expand.grid( t=seq(-1,20), z=c(5,10,20,40,80,160,320,640),degreedays=seq(0, 5000, by=100) )
toplot$predictions = predict(fit, newdata=toplot, type="response", se.fit=FALSE )
plot( predictions ~ z, toplot[ which( {toplot$t==min(toplot$t)} & {toplot$degreedays==min(toplot$degreedays)} ), ], type="b" )
plot( predictions ~ t, toplot[ which( {toplot$z==min(toplot$z)} & {toplot$degreedays==min(toplot$degreedays)} ), ], type="b" )
plot( predictions ~ degreedays, toplot[ which( {toplot$z==min(toplot$z)} & {toplot$t==min(toplot$t)} ), ], type="b")
# predicted probabilities of observing cod, given covariates (temperature, depth, etc)
APS = aegis_prediction_surface( aegis_data=res$means )
APS$data_offset=1
APS$yr = APS$year
APS$yr_factor = factor( APS$year, levels=p$yrs)
APS$iyr = match(APS$yr_factor, p$yrs)
APS$istrata = match( APS$AUID, sppoly$AUID )
predictions = predict(fit, APS, type="response", se.fit=TRUE )
APS$predictions = predictions$fit
APS$predictions.se = predictions$se.fit
# reformat predictions into matrix form
out = matrix(NA, nrow=length(sppoly$AUID), ncol=length(p$yrs), dimnames=list( sppoly$AUID, p$yrs) )
out[ cbind(APS$istrata, APS$iyr) ] = APS$predictions
RES$habitat_glm = colSums( {out * sppoly$au_sa_km2 }[sppoly$strata_to_keep,], na.rm=TRUE ) /sum(sppoly$au_sa_km2[sppoly$strata_to_keep]) # sa weighted average prob habitat
# map it onto strata means of temperature and depth
aps = APS[ APS$year==2017, ]
iy = match( as.character(sppoly$AUID), aps$AUID )
vn = "pred"
sppoly[,vn] = APS$predictions[iy]
brks = interval_break(X= sppoly[[vn]], n=length(p$mypalette), style="quantile")
spplot( sppoly, vn, col.regions=p$mypalette, main=vn, at=brks, sp.layout=p$coastLayout, col="transparent" )
# ------------------------------------------------
# Model 5b: habitat model with a smoothed covariate effect
fit = mgcv::gam(
formula = pa ~ 1 + s(t, k=3, bs="ts") + s(z, k=3, bs="ts") + s(degreedays, k=3, bs="ts"),
family=binomial(link="logit"),
data=set
)
inverse.logit = function( x ) {
# x should be the log odds ratio
oddsratio = exp(x)
prob = oddsratio / (1 + oddsratio )
return (prob)
}
if (0) {
fnx = file.path( project.datadirectory( "carstm" ), "fit_habitat_gam.rdata" )
save( fit, file=fnx )
# load(fnx)
}
plot(fit, all.terms=TRUE, trans=inverse.logit, seWithMean=TRUE, jit=TRUE, rug=TRUE )
s = summary(fit)
AIC(fit) # 10579 .. a little better than the glm
toplot = expand.grid( t=seq(-1,20), z=c(5,10,20,40,80,160,320,640),degreedays=seq(0, 5000, by=100) )
toplot$predictions = predict(fit, newdata=toplot, type="response", se.fit=FALSE )
plot( predictions ~ z, toplot[ which( {toplot$t==min(toplot$t)} & {toplot$degreedays==min(toplot$degreedays)} ), ], type="b" )
plot( predictions ~ t, toplot[ which( {toplot$z==min(toplot$z)} & {toplot$degreedays==min(toplot$degreedays)} ), ], type="b" )
plot( predictions ~ degreedays, toplot[ which( {toplot$z==min(toplot$z)} & {toplot$t==min(toplot$t)} ), ], type="b")
# predicted probabilities of observing cod, given temperature and depth
APS = aegis_prediction_surface( aegis_data=res$means )
APS$data_offset=1
APS$yr = APS$year
APS$yr_factor = factor( APS$year, levels=p$yrs)
APS$iyr = match(APS$yr_factor, p$yrs)
APS$istrata = match( APS$AUID, sppoly$AUID )
predictions = predict(fit, APS, type="response", se.fit=TRUE )
APS$predictions = predictions$fit
APS$predictions.se = predictions$se.fit
# reformat predictions into matrix form
out = matrix(NA, nrow=length(sppoly$AUID), ncol=length(p$yrs), dimnames=list( sppoly$AUID, p$yrs) )
out[ cbind(APS$istrata, APS$iyr) ] = APS$predictions
RES$habitat_gam = colSums( {out * sppoly$au_sa_km2 }[sppoly$strata_to_keep,], na.rm=TRUE ) /sum(sppoly$au_sa_km2[sppoly$strata_to_keep]) # sa weighted average prob habitat
# map it
iy = which( APS$year=="2017")
it = match( as.character(sppoly$AUID), APS$AUID[iy] )
vn = "pred"
sppoly[,vn] = APS$predictions[iy][it]
brks = interval_break(X= sppoly[[vn]], n=length(p$mypalette), style="quantile")
spplot( sppoly, vn, col.regions=p$mypalette, main=vn, at=brks, sp.layout=p$coastLayout, col="transparent" )
# ------------------------------------------------
# Model 5c: as above but via INLA ... very slow
## similar to GAM
APS = aegis_prediction_surface( aegis_data=res$means )
APS$data_offset=1
APS$pa = NA # what we are trying to predict
APS$tag = "predictions"
APS$yr = APS$year
APS$yr_factor = factor( APS$year, levels=p$yrs)
basic_vars = unique(c( "pa", "t", "z", "degreedays", "data_offset", "tag", "yr", "AUID"))
M = rbind( set[, basic_vars], APS[,basic_vars] )
M$t[!is.finite(M$t)] = median(M$t, na.rm=TRUE ) # missing data .. quick fix .. do something better for
M$z[!is.finite(M$z)] = median(M$z, na.rm=TRUE ) # missing data .. quick fix .. do something better for
M$yr_factor = factor( M$yr, levels=p$yrs )
M$AUID = factor( M$AUID, levels=levels(sppoly$AUID ))
M$ti = discretize_data( M$t, p$discretization$t )
M$zi = discretize_data( M$z, p$discretization$z )
M$di = discretize_data( M$degreedays, p$discretization$degreedays )
fit = inla(
formula = pa ~ 1
+ f(ti, model="rw2", scale.model=TRUE, diagonal=1e-5, hyper=H$prec)
+ f(zi, model="rw2", scale.model=TRUE, diagonal=1e-5, hyper=H$prec)
+ f(di, model="rw2", scale.model=TRUE, diagonal=1e-5, hyper=H$prec),
family="binomial", # alternates family="zeroinflatedbinomial0", family="zeroinflatedbinomial1",
data=M,
control.family=list(control.link=list(model="logit")),
control.compute=list(cpo=TRUE, waic=TRUE, dic=TRUE, config=TRUE),
control.results=list(return.marginals.random=TRUE, return.marginals.predictor=TRUE ),
control.predictor=list(compute=TRUE, link=1 ), # compute=TRUE on each data location
control.fixed=H$fixed, # priors for fixed effects
control.inla=list( correct=TRUE, correct.verbose=FALSE ), # strategy="laplace", cutoff=1e-6,
verbose=TRUE
)
if (0) {
fnx = file.path( project.datadirectory( "carstm" ), "fit_habitat_inla.rdata" )
save( fit, file=fnx )
# load(fnx)
}
plot(fit )
s = summary(fit)
s$dic$dic # 10585 .. not sure why ..
s$dic$p.eff # 17.73
APS = cbind( APS, fit$summary.fitted.values[ which(M$tag=="predictions"), ] )
APS$iyr = match(APS$yr_factor, p$yrs)
APS$istrata = match( APS$AUID, sppoly$AUID )
# reformat predictions into matrix form
out = matrix(NA, nrow=length(sppoly$AUID), ncol=length(p$yrs), dimnames=list( sppoly$AUID, p$yrs) )
out[ cbind(APS$istrata, APS$iyr) ] = APS$mean
RES$habitat_inla = colSums( {out * sppoly$au_sa_km2 }[sppoly$strata_to_keep,], na.rm=TRUE ) /sum(sppoly$au_sa_km2[sppoly$strata_to_keep]) # sa weighted average prob habitat
# map it
vn = "pred"
sppoly[,vn] = out[,"2017"]
brks = interval_break(X= sppoly[[vn]], n=length(p$mypalette), style="quantile")
spplot( sppoly, vn, col.regions=p$mypalette, main=vn, at=brks, sp.layout=p$coastLayout, col="transparent" )
# NOTE most of the decline occured when "habitat" was stable !
# NOTE habitat has become more variable since 1995
# NOTE habitat has declined in 2017
# to do : compute SE's and add to the graph
## -------------------------------------------------------
# bym, iid_year
# Model XX:
APS = aegis_prediction_surface( aegis_data=res$means )
APS$data_offset=1
APS$pa = NA # what we are trying to predict
APS$tag = "predictions"
APS$yr = APS$year
APS$yr_factor = factor( APS$year, levels=p$yrs)
basic_vars = unique(c( "pa", "t", "z", "degreedays", "data_offset", "tag", "yr", "AUID"))
M = rbind( set[, basic_vars], APS[,basic_vars] )
M$t[!is.finite(M$t)] = median(M$t, na.rm=TRUE ) # missing data .. quick fix .. do something better for
M$z[!is.finite(M$z)] = median(M$z, na.rm=TRUE ) # missing data .. quick fix .. do something better for
M$iid_error = 1:nrow(M)
M$yr_factor = factor( as.character(M$yr) )
M$AUID = factor( M$AUID, levels=levels(sppoly$AUID ))
M$strata = as.numeric( M$AUID)
M$year = as.numeric( M$yr_factor)
M$ti = discretize_data( M$t, p$discretization$t )
M$zi = discretize_data( M$z, p$discretization$z )
M$di = discretize_data( M$degreedays, p$discretization$degreedays )
fit = inla(
formula = pa ~ 1
+ f(iid_error, model="iid", hyper=H$iid)
+ f(ti, model="rw2", scale.model=TRUE, hyper=H$rw2)
+ f(zi, model="rw2", scale.model=TRUE, hyper=H$rw2)
+ f(di, model="rw2", scale.model=TRUE, hyper=H$rw2)
+ f(year, model="iid", hyper=H$iid)
+ f(strata, model="bym2", graph=slot(sppoly, "nb"), scale.model=TRUE, constr=TRUE, hyper=H$bym2),
family="binomial", # alternates family="zeroinflatedbinomial0", family="zeroinflatedbinomial1",
data=M,
control.family=list(control.link=list(model="logit")),
control.compute=list(cpo=TRUE, waic=TRUE, dic=TRUE, config=TRUE),
control.results=list(return.marginals.random=TRUE, return.marginals.predictor=TRUE ),
control.predictor=list(compute=TRUE, link=1 ), # compute=TRUE on each data location
control.fixed=H$fixed, # priors for fixed effects
control.inla=list( correct=TRUE, correct.verbose=FALSE ), # strategy="laplace", cutoff=1e-6,
verbose=TRUE
)
if (0) {
fnx = file.path( project.datadirectory( "carstm" ), "fit_habitat_strata_CAR.yr_iid.rdata" )
save( fit, file=fnx )
# load(fnx)
}
plot(fit )
s = summary(fit)
s$dic$dic #8885
s$dic$p.eff #163.8
APS = cbind( APS, fit$summary.fitted.values[ which(M$tag=="predictions"), ] )
APS$iyr = match(APS$yr_factor, p$yrs)
APS$istrata = match( APS$AUID, sppoly$AUID )
# reformat predictions into matrix form
out = matrix(NA, nrow=length(sppoly$AUID), ncol=length(p$yrs), dimnames=list( sppoly$AUID, p$yrs) )
out[ cbind(APS$istrata, APS$iyr) ] = APS$mean
RES$habitat_strata_CAR.yr_iid = colSums( {out * sppoly$au_sa_km2 }[sppoly$strata_to_keep,], na.rm=TRUE ) /sum(sppoly$au_sa_km2[sppoly$strata_to_keep]) # sa weighted average prob habitat
# map it
vn = "pred"
sppoly[,vn] = out[,"2017"]
brks = interval_break(X= sppoly[[vn]], n=length(p$mypalette), style="quantile")
spplot( sppoly, vn, col.regions=p$mypalette, main=vn, at=brks, sp.layout=p$coastLayout, col="transparent" )
## -------------------------------------------------------
# bym, iid_year
# Model XX:
APS = aegis_prediction_surface( aegis_data=res$means )
APS$data_offset=1
APS$pa = NA # what we are trying to predict
APS$tag = "predictions"
APS$yr = APS$year
APS$yr_factor = factor( APS$year, levels=p$yrs)
basic_vars = unique(c( "pa", "t", "z", "degreedays", "data_offset", "tag", "yr", "AUID"))
M = rbind( set[, basic_vars], APS[,basic_vars] )
M$t[!is.finite(M$t)] = median(M$t, na.rm=TRUE ) # missing data .. quick fix .. do something better for
M$z[!is.finite(M$z)] = median(M$z, na.rm=TRUE ) # missing data .. quick fix .. do something better for
M$iid_error = 1:nrow(M)
M$yr_factor = factor( as.character(M$yr) )
M$AUID = factor( M$AUID, levels=levels(sppoly$AUID ))
M$strata = as.numeric( M$AUID)
M$year = as.numeric( M$yr_factor)
M$ti = discretize_data( M$t, p$discretization$t )
M$zi = discretize_data( M$z, p$discretization$z )
M$di = discretize_data( M$degreedays, p$discretization$degreedays )
# 28404.251 seconds
fit = inla(
formula = pa ~ 1
+ f(iid_error, model="iid", hyper=H$iid)
+ f(ti, model="rw2", scale.model=TRUE, hyper=H$rw2)
+ f(zi, model="rw2", scale.model=TRUE, hyper=H$rw2)
+ f(di, model="rw2", scale.model=TRUE, hyper=H$rw2)
+ f(year, model="iid", hyper=H$iid)
+ f(strata, model="bym2", graph=slot(sppoly, "nb"), group=year, scale.model=TRUE, constr=TRUE, hyper=H$bym2),
family="binomial", # alternates family="zeroinflatedbinomial0", family="zeroinflatedbinomial1",
data=M,
control.family=list(control.link=list(model="logit")),
control.compute=list(cpo=TRUE, waic=TRUE, dic=TRUE, config=TRUE),
control.results=list(return.marginals.random=TRUE, return.marginals.predictor=TRUE ),
control.predictor=list(compute=TRUE, link=1 ), # compute=TRUE on each data location
control.fixed=H$fixed, # priors for fixed effects
control.inla=list( correct=TRUE, correct.verbose=FALSE ), # strategy="laplace", cutoff=1e-6,
verbose=TRUE
)
if (0) {
fnx = file.path( project.datadirectory( "carstm" ), "fit_habitat_strata_CAR_yr.yr_iid.rdata" )
save( fit, file=fnx )
# load(fnx)
}
plot(fit )
s = summary(fit)
s$dic$dic # 8730
s$dic$p.eff # 399.4
APS = cbind( APS, fit$summary.fitted.values[ which(M$tag=="predictions"), ] )
APS$iyr = match(APS$yr_factor, p$yrs)
APS$istrata = match( APS$AUID, sppoly$AUID )
# reformat predictions into matrix form
out = matrix(NA, nrow=length(sppoly$AUID), ncol=length(p$yrs), dimnames=list( sppoly$AUID, p$yrs) )
out[ cbind(APS$istrata, APS$iyr) ] = APS$mean
RES$habitat_strata_CAR_yr.yr_iid = colSums( {out * sppoly$au_sa_km2 }[sppoly$strata_to_keep,], na.rm=TRUE ) /sum(sppoly$au_sa_km2[sppoly$strata_to_keep]) # sa weighted average prob habitat
# map it
vn = "pred"
sppoly[,vn] = out[,"2017"]
brks = interval_break(X= sppoly[[vn]], n=length(p$mypalette), style="quantile")
spplot( sppoly, vn, col.regions=p$mypalette, main=vn, at=brks, sp.layout=p$coastLayout, col="transparent" )
# fn2="habitat_strata_CAR_yr.yr_iid.rdata"
# save(fit, file=fn2)
# load( fn2)
######
if (0) {
fn = file.path( project.datadirectory( "carstm" ), "RES.rdata" )
# save(RES, file=fn)
# load(fn)
}
# RES$habitat_strata_CAR.yr_iid = RES$habitat_bym_yriid
dev.new(width=11, height=7)
# col = c("slategray", "turquoise", "darkorange", "green", "blue", "darkred", "cyan", "darkgreen", "purple" )
col = c( "darkorange", "green", "blue", "cyan", "darkgreen" )
pch = c(20, 21, 22, 23, 24)#, 25, 26, 27, 20)
lty = c(1, 3, 4, 5, 6)#, 7, 1, 3, 4 )
lwd = c(4, 4, 4, 4, 4)#, 4, 4, 4, 4 )
type =c("l", "l", "l", "l", "l")#, "l", "l", "l", "l")
legend=c("GLM", "GAM", "INLA", "INLA CAR", "INLA CAR|year")#, "INLA Envir AR1 CAR|year", "INLA Envir AR1|strata CAR", "INLA Envir AR1|strata CAR|year", "INLA Envir CAR|year")
plot( habitat_glm ~ yr, data=RES, lty=lty[1], lwd=lwd[1], col=col[1], pch=pch[1], type=type[1], ylim=c(0.375,0.825), xlab="Year", ylab="Probability")
lines( habitat_gam ~ yr, data=RES, lty=lty[2], lwd=lwd[2], col=col[2], pch=pch[2], type=type[2])
lines( habitat_inla ~ yr, data=RES, lty=lty[3], lwd=lwd[3], col=col[3], pch=pch[3], type=type[3])
lines( habitat_strata_CAR.yr_iid ~ yr, data=RES, lty=lty[4], lwd=lwd[4], col=col[4], pch=pch[4], type=type[4]) # yr_iid
lines( habitat_strata_CAR_yr.yr_iid ~ yr, data=RES, lty=lty[5], lwd=lwd[5], col=col[5], pch=pch[5], type=type[5])
# lines( INLA.Envir.AR1.CAR_year ~ yr, data=RES, lty=lty[6], lwd=lwd[6], col=col[6], pch=pch[6], type=type[6])
# lines( INLA.Envir.AR1_strata.CAR ~ yr, data=RES, lty=lty[7], lwd=lwd[7], col=col[7], pch=pch[7], type=type[7])
# lines( INLA.Envir.AR1_strata.CAR_year ~ yr, data=RES, lty=lty[8], lwd=lwd[8], col=col[8], pch=pch[8], type=type[8])
# lines( INLA.Envir.yr_iid.CAR_year ~ yr, data=RES, lty=lty[9], lwd=lwd[9], col=col[9], pch=pch[9], type=type[9])
legend("topright", legend=legend, lty=lty, col=col, lwd=lwd )
# end
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