CATLVM User Guide for Latent Transition Analysis

Transcription

1 CATLVM User Guide for Latent Transition Analysis Dimension Term Type Definition nkase Integer scalar Number of subject nstr Integer scalar Number of subgroups nc Integer scalar Number of latent subgroups ns Integer scalar Number of latent dynamic statuses nt Integer scalar Number of time points nsi Integer scalar Number of manifest items nrs Integer vector of length nsi Number of categories for each item ncov$delta Integer scalar Number of covariates for DELTA ncov$tau Integer scalar Number of covariates for TAU Parameters for an LTA Parameter Array dimension Definition param$lta$big.rho nsi max(nrs) ns nt nc nstr Item response probabilities within a latent status at time t for each latent class and subgroup param$lta$delta nt ns nc nstr Status prevalence for each latent class and subgroup Param$lta$tau ns ns nt-1 nc nstr Transitional probability of status membership param$lta$beta$delta ncov$delta ns nstr Logistic regression coefficients to predict status membership at the initial time param$lta$beta$tau ncov$tau ns ns nt- 1 nc nstr Logistic regression coefficients to predict the transition of statuses 1

2 1. Loading the data Data should be loaded in a list. Data-list consists of following: data$is.grp (logical) True if analysis will use group variable. data$group (optional) An integer vector of group variable with length of nkase. Integer values should start from 1. If data$is.grp = TRUE, then data$group should be provided. data$lta$si Observed manifest items to measure latent statuses. It should be an array size of nkase nsi nt. The values must be integer starting from 1. Missing values should be coded as NA. data$lta$cov$delta (optional) Observed covariates to predict latent status membership at the initial time point. It should be a matrix size of nkase ncov$delta. data$lta$cov$tau (optional) Observed covariates to predict transition of latent status membership. It should be an array size of nkase ncov$tau (nt-1). 2. Model configuration Model configuration should be saved in a list. Model-list consists of following: model$lta$is.lta (logical) True if you want to fit a latent transition analysis. model$lta$ns Number of latent statuses. model$lta$nt Number of time points. model$lta$nrs Integer vector. Number of response categories for each item. The length of vector should be equal to the number of items (i.e., nsi). 2

3 3. Parameter constraints (optional) Parameter constraints should be saved in a list. Constraint-list consists of following: constraint$lta$equal$big.rho$group (logical) True if param$lta$big.rho are constrained to be equal across group variable. Default value = FALSE. constraint$lta$equal$big.rho$time (logical) True if param$lta$big.rho are constrained to be equal across time points. Default value = FALSE. constraint$lta$equal$big.rho$class (logical) True if param$lta$big.rho are constrained to be equal across latent classes (latent group variable). It will be used only when model$lca$is.lca = TRUE. Default value = FALSE. constraint$lta$big.rho Integer array of 1 or 0. The elements of constraint$lta$big.rho with one represent that the corresponding param$lta$big.rho will be freely estimated. The elements of constraint$lta$big.rho with 0 means that the corresponding param$lta$big.rho will be fixed as zero. Dimension of constraint$lta$big.rho is equal to param$lta$big.rho. Default setting is to freely estimate. constraint$lta$delta Integer array of 1 or 0. The array displays the constraint of param$lta$delta at Time 1. The elements of constraint$lta$delta with 1 represents that the corresponding param$lta$delta will be freely estimated. The elements of constraint$lta$delta with 0 means that the corresponding param$lta$delta will be fixed as zero. Dimension of constraint$lta$delta is ns nc nstr. Default setting is to freely estimate. constraint$lta$tau Integer array of 1 or 0. The elements of constraint$lta$taua with 1 represents that the corresponding param$lta$tau will be freely estimated. The elements of constraint$lta$tau with 0 means that the corresponding param$lta$tau will be 3

4 fixed as zero. Dimension of constraint$lta$tau is equal to param$lta$tau. Default setting is to freely estimate. 4. Starting values (optional) Starting-value configuration should be saved in a list. Starval-list consists of following: starval$is.random (logical, optional) True if you want to generate random starting values. Default value = TRUE. starval$param$lta (optional) Starting values provided by users. If starval$is.random = FALSE, then users should provide starting values for LTA parameters. The dimension starval$param$lta is equal to param$lta. starval$ntry (optional) Number of sets of different starting values that the program will try. This is to assure global maximum at the final solution. Default value = 10. starval$try.maxits (optional) Maximum number of iterations for each set of starting values. Program will pick the set starting values which leads to the largest likelihood after this trial iteration. Default value = Iteration (optional) Iteration configuration should be saved in a list. Iteration-list consists of following: iteration$maxits (optional) Maximum number of iterations. Default value = iteration$eps (optional) Convergence criteria. Default value = 1e-6. 4

5 An example of latent transition analysis using CATLVM This is a three-class LTA with logistic regression. Three latent classes are measured by six binary items from two subgroups. nkase = 500 nstr = 1 nc = 1 nt = 3 ns = 3 nsi = 4 nrc = c(2, 2, 2, 2) ## Items of first five subjects LTA.sItem[1:5,,],, 1 In R Console [,3] [,4] [1,] [2,] [3,] [4,] NA [5,] ,, 2 [,3] [,4] [1,] NA [2,] [3,] [4,] [5,] NA,, 3 5

6 [,3] [,4] [1,] NA [2,] [3,] [4,] [5,] ## DELTA cvariate of first five subjects LTA.covariate$delta[1:5,] [1] ## TAU cvariate of first five subjects LTA.covariate$tau[1:5,,] [1,] [2,] [3,] [4,] [5,] ############### ## LOAD DATA ## ############### data <- list() data$lta$si <- LTA.sItem ########################## ## SPECIFY AN LTA MODEL ## ########################## model <- list() model$lta$is.lta <- TRUE model$lta$ns <- 3 model$lta$nrs <- c(2, 2, 2, 2) ############################# ## RESTRICT RHO PARAMETERS ## ############################# constraint <- list() 6

7 constraint$lta$equal$big.rho$time <- TRUE ########################## ## STARTING VALUE SETUP ## ########################## starval <- list() starval$is.random <- TRUE ##################### ## RUNNING PROGRAM ## ##################### LTA.1 <- cat.lvm(data=data, model=model, starval=starval, + constraint=constraint) Trying to find the best set of starting values... SET: SET: SET: SET: SET: SET: SET: SET: SET: SET: Done. SET 3 selected. Starting main iteration e e e-07 OK, converged at 166 7

8 summary(lta.1) Length Class Mode model 3 -none- list iteration 6 -none- list param 1 -none- list constraint 1 -none- list prior 1 -none- list ######################### ## ESTIMATED PRAMETERS ## ######################### LTA.1$param $lta $lta$big.rho,, Stage.1, Time.1,, sitem sitem sitem sitem ,, Stage.2, Time.1,, sitem sitem sitem sitem ,, Stage.3, Time.1,, sitem sitem sitem sitem

9 ,, Stage.1, Time.2,, sitem sitem sitem sitem ,, Stage.2, Time.2,, sitem sitem sitem sitem ,, Stage.3, Time.2,, sitem sitem sitem sitem ,, Stage.1, Time.3,, sitem sitem sitem sitem ,, Stage.2, Time.3,, sitem sitem sitem

10 sitem ,, Stage.3, Time.3,, sitem sitem sitem sitem $lta$delta,,, Time Time Time $lta$tau,, Time.2,, Stage Stage Stage ,, Time.3,, Stage Stage Stage

11 ############################## ## INFO ABOUT EM ITERATIONS ## ############################## LTA.1$iteration $maxits [1] 2500 $eps [1] 1e-06 $niter [1] 166 $maxdiff [1] e-07 $converged [1] TRUE $llvec [1] ################################# ## INFO ABOUT FITTED LTA MODEL ## ################################# LTA.1$model $lta $lta$is.lta [1] TRUE $lta$ns [1] 3 $lta$nrs [1] $lta$nkase 11

12 [1] 50 $lta$nstr [1] 1 $lta$nsi [1] 4 $lta$nt [1] 3 $lta$nc [1] 1 $lta$ncov $lta$ncov$delta [1] 0 $lta$ncov$tau [1] 0 $lca $lca$is.lca [1] FALSE $lca$nc [1] 1 $lcpa $lcpa$is.lcpa [1] FALSE ###################################### 12

13 ## INFO ABOUT PARAMETER CONSTRAINTS ## ###################################### LTA.1$constraint $lta $lta$equal $lta$equal$big.rho $lta$equal$big.rho$group [1] FALSE $lta$equal$big.rho$time [1] TRUE $lta$equal$big.rho$class [1] FALSE $lta$big.rho,, Stage.1, Time.1,, sitem sitem sitem sitem.4 1 1,, Stage.2, Time.1,, sitem sitem sitem sitem.4 1 1,, Stage.3, Time.1,, sitem

14 sitem sitem sitem.4 1 1,, Stage.1, Time.2,, sitem sitem sitem sitem.4 1 1,, Stage.2, Time.2,, sitem sitem sitem sitem.4 1 1,, Stage.3, Time.2,, sitem sitem sitem sitem.4 1 1,, Stage.1, Time.3,, sitem sitem sitem sitem.4 1 1,, Stage.2, Time.3,, 14

15 sitem sitem sitem sitem.4 1 1,, Stage.3, Time.3,, sitem sitem sitem sitem $lta$delta,, Stage.1 1 Stage.2 1 Stage.3 1 $lta$tau,, Time.2,, Stage Stage Stage ,, Time.3,, Stage Stage Stage

16 ##################################### ## ADD DELTA COVARIATES TO THE LTA ## ##################################### data$lta$cov$delta <- LTA.covariate$delta ##################### ## RUNNING PROGRAM ## ##################### LTA.REG.1 <- cat.lvm(data=data, model=model, starval=starval, + constraint=constraint) Trying to find the best set of starting values... SET: SET: SET: SET: SET: SET: SET: SET: SET: SET: Done. SET 5 selected. Starting main iteration e e e e-07 OK, converged at 71 16

17 ################################### ## ADD TAU COVARIATES TO THE LTA ## ################################### data$lta$cov$tau <- LTA.covariate$tau ###################################################### ## FIX SOME TAUs AS ZERO TO AVOID BOUNDARY SOLUTION ## ###################################################### constraint$lta$tau <- LTA.REG.1$constraint$lta$TAU w <- LTA.REG.1$param$lta$tau < 0.1 constraint$lta$tau[w] <- 0 ##################### ## RUNNING PROGRAM ## ##################### LTA.REG.2 <- cat.lvm(data=data, model=model, starval=starval, + constraint=constraint) Trying to find the best set of starting values... SET: SET: SET: SET: SET: SET: SET: SET: SET: SET: Done. SET 9 selected. Starting main iteration

18 e e e e-07 OK, converged at 32 ######################### ## ESTIMATED PRAMETERS ## ######################### LTA.REG.2$param $lta $lta$big.rho,, Stage.1, Time.1,, sitem sitem sitem sitem ,, Stage.2, Time.1,, sitem sitem sitem sitem ,, Stage.3, Time.1,, sitem sitem sitem sitem

19 ,, Stage.1, Time.2,, sitem sitem sitem sitem ,, Stage.2, Time.2,, sitem sitem sitem sitem ,, Stage.3, Time.2,, sitem sitem sitem sitem ,, Stage.1, Time.3,, sitem sitem sitem sitem ,, Stage.2, Time.3,, sitem sitem sitem

20 sitem ,, Stage.3, Time.3,, sitem sitem sitem sitem $lta$delta,,, Time Time Time $lta$tau,, Time.2,, Stage Stage Stage ,, Time.3,, Stage Stage Stage $lta$beta $lta$beta$delta 20

21 ,,, Int cov.delta $lta$beta$tau,, Stage.1, Time.2,, Int. 0 NA NA cov.tau.1 0 NA NA,, Stage.2, Time.2,, Int. NA cov.tau.1 NA ,, Stage.3, Time.2,, Int. NA 0 NA cov.tau.1 NA 0 NA,, Stage.1, Time.3,, Int NA cov.tau NA,, Stage.2, Time.3,, Int. NA cov.tau.1 NA

22 ,, Stage.3, Time.3,, Int cov.tau ################################################# ## USE ESTIMATED PARAMETERS AS STARTING VALUES ## ################################################# starval <- list() starval$is.random <- FALSE starval$param <- LTA.REG.2$param LTA.REG.33 <- cat.lvm(data=data, model=model, starval=starval, + constraint=constraint) Starting main iteration e-07 OK, converged at 1 22