# Fit closed population abundance models for ``traditional'' capture-mark-recapture data consisting of a single mark type This function fits closed population abundance models for ``traditional'' capture-mark-recapture data consisting of a single mark type using Bayesian analysis methods. Markov chain Monte Carlo (MCMC) is used to draw samples from the joint posterior distribution. ```r markClosed( Enc.Mat, covs = data.frame(), mod.p = ~1, parms = c("pbeta", "N"), nchains = 1, iter = 12000, adapt = 1000, bin = 50, thin = 1, burnin = 2000, taccept = 0.44, tuneadjust = 0.95, proppbeta = 0.1, propzp = 1, propsigmap = 1, npoints = 500, a = 25, mu0 = 0, sigma2_mu0 = 1.75, initial.values = NULL, printlog = FALSE, ... ) ``` ## Arguments - `Enc.Mat`: A matrix of observed encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions. With a single mark type, encounter histories consist of only non-detections (0) and type 1 encounters (1). - `covs`: A data frame of temporal covariates for detection probabilities (ignored unless `mms=NULL`). The number of rows in the data frame must equal the number of sampling occasions. Covariate names cannot be "time", "age", or "h"; these names are reserved for temporal, behavioral, and individual effects when specifying `mod.p` and `mod.phi`. - `mod.p`: Model formula for detection probability. For example, `mod.p=~1` specifies no effects (i.e., intercept only), `mod.p~time` specifies temporal effects, `mod.p~c` specifies behavioral reponse (i.e., trap "happy" or "shy"), `mod.p~h` specifies individual heterogeneity, and `mod.p~time+c` specifies additive temporal and behavioral effects. - `parms`: A character vector giving the names of the parameters and latent variables to monitor. Possible parameters are logit-scale detection probability parameters ("`pbeta`"), population abundance ("`N`"), logit-scale individual heterogeneity variance term ("`sigma2_zp`"), and logit-scale individual effects ("`zp`"). The log posterior density ("`logPosterior`") may also be monitored. Setting `parms="all"` monitors all possible parameters and latent variables. - `nchains`: The number of parallel MCMC chains for the model. - `iter`: The number of MCMC iterations. - `adapt`: The number of iterations for proposal distribution adaptation. If `adapt = 0` then no adaptation occurs. - `bin`: Bin length for calculating acceptance rates during adaptive phase (`0 < bin <= iter`). - `thin`: Thinning interval for monitored parameters. - `burnin`: Number of burn-in iterations (`0 <= burnin < iter`). - `taccept`: Target acceptance rate during adaptive phase (`0 < taccept <= 1`). Acceptance rate is monitored every `bin` iterations. Default is `taccept = 0.44`. - `tuneadjust`: Adjustment term during adaptive phase (`0 < tuneadjust <= 1`). If acceptance rate is less than `taccept`, then proposal term (`proppbeta`, `propzp`, or `propsigmap`) is multiplied by `tuneadjust`. If acceptance rate is greater than or equal to `taccept`, then proposal term is divided by `tuneadjust`. Default is `tuneadjust = 0.95`. - `proppbeta`: Scaler or vector (of length k) specifying the initial standard deviation of the Normal(pbeta[j], proppbeta[j]) proposal distribution. If `proppbeta` is a scaler, then this value is used for all j = 1, ..., k. Default is `proppbeta = 0.1`. - `propzp`: Scaler or vector (of length M) specifying the initial standard deviation of the Normal(zp[i], propzp[i]) proposal distribution. If `propzp` is a scaler, then this value is used for all i = 1, ..., M individuals. Default is `propzp = 1`. - `propsigmap`: Scaler specifying the initial Gamma(shape = 1/`propsigmap`, scale = sigma_zp * `propsigmap`) proposal distribution for sigma_zp = sqrt(sigma2_zp). Default is `propsigmap=1`. - `npoints`: Number of Gauss-Hermite quadrature points to use for numerical integration. Accuracy increases with number of points, but so does computation time. - `a`: Scale parameter for [sigma_z] ~ half-Cauchy(a) prior for the individual hetegeneity term sigma_zp = sqrt(sigma2_zp). Default is ``uninformative'' `a = 25`. - `mu0`: Scaler or vector (of length k) specifying mean of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If `mu0` is a scaler, then this value is used for all j = 1, ..., k. Default is `mu0 = 0`. - `sigma2_mu0`: Scaler or vector (of length k) specifying variance of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If `sigma2_mu0` is a scaler, then this value is used for all j = 1, ..., k. Default is `sigma2_mu0 = 1.75`. - `initial.values`: Optional list of `nchain` list(s) specifying initial values for "`pbeta`", "`zp`", "`sigma2_zp`", and "`N`". Default is `initial.values = NULL`, which causes initial values to be generated automatically. - `printlog`: Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when `nchains=1`. Updates are printed to log file as 1% increments of `iter` of each chain are completed. With >1 chains, setting `printlog=TRUE` is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when `printlog=FALSE`. Default is `printlog=FALSE`. - `...`: Additional "`parameters`" arguments for specifying `mod.p`. See `make.design.data`. ## Returns A list containing the following: - **mcmc**: Markov chain Monte Carlo object of class `mcmc.list`. - **mod.p**: Model formula for detection probability (as specified by `mod.p` above). - **mod.delta**: Formula always `NULL`; only for internal use in `multimodelClosed`. - **DM**: A list of design matrices for detection probability generated for model `mod.p`, where DM$p is the design matrix for initial capture probability (p) and DM$c is the design matrix for recapture probability (c). - **initial.values**: A list containing the parameter and latent variable values at iteration `iter` for each chain. Values are provided for "`pbeta`", "`zp`", "`sigma2_zp`", and "`N`". - **mms**: An object of class `multimarksetup` ## Details The first time `markClosed` (or `markCJS`) is called, it will likely produce a firewall warning alerting users that R has requested the ability to accept incoming network connections. Incoming network connections are required to use parallel processing as implemented in `markClosed`. Note that setting `parms="all"` is required for any `markClosed` model output to be used in `multimodelClosed`. ## Examples ```r # This example is excluded from testing to reduce package check time # Example uses unrealistically low values for nchain, iter, and burnin #Run single chain using the default model for simulated ``traditional'' data data<-simdataClosed(delta_1=1,delta_2=0)$Enc.Mat sim.dot<-markClosed(data) #Posterior summary for monitored parameters summary(sim.dot$mcmc) plot(sim.dot$mcmc) ``` ## See Also `multimodelClosed` ## Author(s) Brett T. McClintock

markClosed function