# Calculate the confidence interval of the results of fitRMU() The data must be a data.frame with the first column being years and two columns for each beach: the average and the se for the estimate. The correspondence between mean, se and density for each rookery are given in the RMU.names data.frame. This data.frame must have a column named mean, another named se and a third named density. If no sd column exists, no sd will be considered for the series and is no density column exists, it will be considered as being "dnorm". In the result list, the mean proportions for each rookeries are in $proportions. The names of beach columns must not begin by T_, SD_, a0_, a1_ or a2_ and cannot be r. A RMU is the acronyme for Regional Managment Unit. See: Wallace, B.P., DiMatteo, A.D., Hurley, B.J., Finkbeiner, E.M., Bolten, A.B., Chaloupka, M.Y., Hutchinson, B.J., Abreu-Grobois, F.A., Amorocho, D., Bjorndal, K.A., Bourjea, J., Bowen, B.W., Dueñas, R.B., Casale, P., Choudhury, B.C., Costa, A., Dutton, P.H., Fallabrino, A., Girard, A., Girondot, M., Godfrey, M.H., Hamann, M., López-Mendilaharsu, M., Marcovaldi, M.A., Mortimer, J.A., Musick, J.A., Nel, R., Seminoff, J.A., Troëng, S., Witherington, B., Mast, R.B., 2010. Regional management units for marine turtles: a novel framework for prioritizing conservation and research across multiple scales. PLoS One 5, e15465. Variance for each value is additive based on both the observed SE (in the RMU.data object) and a constant value dependent on the rookery when model.SD is equal to "Rookery-constant". The value is a global constant when model.SD is "global-constant". The value is proportional to the observed number of nests when model.SD is "global-proportional" with aSD_*observed+SD_ with aSD_ and SD_ being fitted values. This value is fixed to zero when model.SD is "Zero". If method is NULL, replicate.CI is set to 0. If method is hessian, it will generate replicate.CI random numbers using Hessian matrix with covariance. If method is se, it will generate replicate.CI random numbers using SE values then without covariance. If method is mcmc, it will generate replicate.CI random numbers using random samples of the MCMC or the regularThin number. If replicate.CI is 0, no CI is estimated, and only point estimation is returned. ```r CI.RMU( result = stop("A result obtained from fitRMU is necessary"), resultMCMC = NULL, method = NULL, chain = 1, replicate.CI = 10000, regularThin = TRUE, probs = c(0.025, 0.5, 0.975), silent = FALSE ) ``` ## Arguments - `result`: A result of fitRMu() - `resultMCMC`: A resuts of fitRMU_MHmcmc() - `method`: Can be NULL, "SE", "Hessian", "MCMC", or "PseudoHessianFromMCMC" - `chain`: Number of MCMC chain to be used - `replicate.CI`: Number of replicates - `regularThin`: If TRUE, use regular thin for MCMC. If a number, take this replicate. - `probs`: The probabilities to return for quantiles - `silent`: If TRUE does not display anything ## Returns Return a list with Total, Proportions, and Numbers ## Details CI.RMU calculates the confidence interval of the results of fitRMU() ## Examples ```r ## Not run: library("phenology") RMU.names.AtlanticW <- data.frame(mean=c("Yalimapo.French.Guiana", "Galibi.Suriname", "Irakumpapy.French.Guiana"), se=c("se_Yalimapo.French.Guiana", "se_Galibi.Suriname", "se_Irakumpapy.French.Guiana"), density=c("density_Yalimapo.French.Guiana", "density_Galibi.Suriname", "density_Irakumpapy.French.Guiana"), stringsAsFactors = FALSE) data.AtlanticW <- data.frame(Year=c(1990:2000), Yalimapo.French.Guiana=c(2076, 2765, 2890, 2678, NA, 6542, 5678, 1243, NA, 1566, 1566), se_Yalimapo.French.Guiana=c(123.2, 27.7, 62.5, 126, NA, 230, 129, 167, NA, 145, 20), density_Yalimapo.French.Guiana=rep("dnorm", 11), Galibi.Suriname=c(276, 275, 290, NA, 267, 542, 678, NA, 243, 156, 123), se_Galibi.Suriname=c(22.3, 34.2, 23.2, NA, 23.2, 4.3, 2.3, NA, 10.3, 10.1, 8.9), density_Galibi.Suriname=rep("dnorm", 11), Irakumpapy.French.Guiana=c(1076, 1765, 1390, 1678, NA, 3542, 2678, 243, NA, 566, 566), se_Irakumpapy.French.Guiana=c(23.2, 29.7, 22.5, 226, NA, 130, 29, 67, NA, 15, 20), density_Irakumpapy.French.Guiana=rep("dnorm", 11), stringsAsFactors = FALSE ) cst <- fitRMU(RMU.data=data.AtlanticW, RMU.names=RMU.names.AtlanticW, colname.year="Year", model.trend="Constant", model.SD="Zero") out.CI.Cst <- CI.RMU(result=cst) cst <- fitRMU(RMU.data=data.AtlanticW, RMU.names=RMU.names.AtlanticW, colname.year="Year", model.trend="Constant", model.SD="Zero", control=list(trace=1, REPORT=100, maxit=500, parscale = c(3000, -0.2, 0.6))) cst <- fitRMU(RMU.data=data.AtlanticW, RMU.names=RMU.names.AtlanticW, colname.year="Year", model.trend="Constant", model.SD="Zero", method=c("Nelder-Mead","BFGS"), control = list(trace = 0, REPORT = 100, maxit = 500, parscale = c(3000, -0.2, 0.6))) expo <- fitRMU(RMU.data=data.AtlanticW, RMU.names=RMU.names.AtlanticW, colname.year="Year", model.trend="Exponential", model.SD="Zero", method=c("Nelder-Mead","BFGS"), control = list(trace = 0, REPORT = 100, maxit = 500, parscale = c(6000, -0.05, -0.25, 0.6))) YS <- fitRMU(RMU.data=data.AtlanticW, RMU.names=RMU.names.AtlanticW, colname.year="Year", model.trend="Year-specific", method=c("Nelder-Mead","BFGS"), model.SD="Zero") YS1 <- fitRMU(RMU.data=data.AtlanticW, RMU.names=RMU.names.AtlanticW, colname.year="Year", model.trend="Year-specific", method=c("Nelder-Mead","BFGS"), model.SD="Zero", model.rookeries="First-order") YS1_cst <- fitRMU(RMU.data=data.AtlanticW, RMU.names=RMU.names.AtlanticW, colname.year="Year", model.trend="Year-specific", model.SD="Constant", model.rookeries="First-order", parameters=YS1$par, method=c("Nelder-Mead","BFGS")) YS2 <- fitRMU(RMU.data=data.AtlanticW, RMU.names=RMU.names.AtlanticW, colname.year="Year", model.trend="Year-specific", model.SD="Zero", model.rookeries="Second-order", parameters=YS1$par, method=c("Nelder-Mead","BFGS")) YS2_cst <- fitRMU(RMU.data=data.AtlanticW, RMU.names=RMU.names.AtlanticW, colname.year="Year", model.trend="Year-specific", model.SD="Constant", model.rookeries="Second-order", parameters=YS1_cst$par, method=c("Nelder-Mead","BFGS")) compare_AIC(Constant=cst, Exponential=expo, YearSpecific=YS) compare_AIC(YearSpecific_ProportionsFirstOrder_Zero=YS1, YearSpecific_ProportionsFirstOrder_Constant=YS1_cst) compare_AIC(YearSpecific_ProportionsConstant=YS, YearSpecific_ProportionsFirstOrder=YS1, YearSpecific_ProportionsSecondOrder=YS2) compare_AIC(YearSpecific_ProportionsFirstOrder=YS1_cst, YearSpecific_ProportionsSecondOrder=YS2_cst) plot(cst, main="Use of different beaches along the time", what="total") plot(expo, main="Use of different beaches along the time", what="total") plot(YS2_cst, main="Use of different beaches along the time", what="total") plot(YS1, main="Use of different beaches along the time") plot(YS1_cst, main="Use of different beaches along the time") plot(YS1_cst, main="Use of different beaches along the time", what="numbers") # Gamma distribution should be used for MCMC outputs RMU.names.AtlanticW <- data.frame(mean=c("Yalimapo.French.Guiana", "Galibi.Suriname", "Irakumpapy.French.Guiana"), se=c("se_Yalimapo.French.Guiana", "se_Galibi.Suriname", "se_Irakumpapy.French.Guiana"), density=c("density_Yalimapo.French.Guiana", "density_Galibi.Suriname", "density_Irakumpapy.French.Guiana")) data.AtlanticW <- data.frame(Year=c(1990:2000), Yalimapo.French.Guiana=c(2076, 2765, 2890, 2678, NA, 6542, 5678, 1243, NA, 1566, 1566), se_Yalimapo.French.Guiana=c(123.2, 27.7, 62.5, 126, NA, 230, 129, 167, NA, 145, 20), density_Yalimapo.French.Guiana=rep("dgamma", 11), Galibi.Suriname=c(276, 275, 290, NA, 267, 542, 678, NA, 243, 156, 123), se_Galibi.Suriname=c(22.3, 34.2, 23.2, NA, 23.2, 4.3, 2.3, NA, 10.3, 10.1, 8.9), density_Galibi.Suriname=rep("dgamma", 11), Irakumpapy.French.Guiana=c(1076, 1765, 1390, 1678, NA, 3542, 2678, 243, NA, 566, 566), se_Irakumpapy.French.Guiana=c(23.2, 29.7, 22.5, 226, NA, 130, 29, 67, NA, 15, 20), density_Irakumpapy.French.Guiana=rep("dgamma", 11) ) cst <- fitRMU(RMU.data=data.AtlanticW, RMU.names=RMU.names.AtlanticW, colname.year="Year", model.trend="Constant", model.SD="Zero") ## End(Not run) ``` ## See Also Other Fill gaps in RMU: `fitRMU()`, `fitRMU_MHmcmc()`, `fitRMU_MHmcmc_p()`, `logLik.fitRMU()`, `plot.fitRMU()` ## Author(s) Marc Girondot

CI.RMU function