CATLVM User Guide for Latent Class-Profile Analysis

Transcription

1 CATLVM User Guide for Latent Class-Profile Analysis Dimension Term Type Definition nkase Integer scalar Number of subject nstr Integer scalar Number of subgroups nc Integer scalar Number of static latent subgroups ns Integer scalar Number of dynamic latent statuses npf Integer scalar Number of latent status-profiles 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$gam.pf Integer scalar Number of covariates for GAM.PF ncov$eta Integer scalar Number of covariates for ETA Parameters for an LCPA Parameter Array dimension Definition param$lcpa$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$lcpa$gam.pf npf nc nstr Status-profile prevalence for each latent class and subgroup Param$lcpa$eta ns nt npf nc nstr Conditional probability of status membership at time t given a latent status profile param$lcpa$beta$gam.pf ncov$gam.pf npf nc nstr Logistic regression coefficients to predict status-profile membership param$lcpa$beta$eta ncov$eta ns nt npf nc nstr Logistic regression coefficients to predict the conditional probability of latent status at time t given a profile 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$lcpa$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$lcpa$cov$gam.pf (optional) Observed covariates to predict latent status-profile membership. It should be a matrix size of nkase ncov$gam.pf. data$lcpa$cov$eta (optional) Observed covariates to predict the conditional probability of status membership at time t given a status-profile. It should be an array size of nkase ncov$eta nt. 2. Model configuration Model configuration should be saved in a list. Model-list consists of following: model$lca$is.lca (logical, optional) True if you want to fit a latent class analysis (see User s manual for latent class analysis). The latent class will be used as a latent group variable. If model$lca$nc (optional) Number of static latent classes. model$lcpa$is.lcpa (logical) True if you want to fit a latent transition analysis. model$lcpa$ns Number of dynamic latent statuses. model$lcpa$npf 2

3 Number of latent status profiles. model$lcpa$nt Number of time points. model$lcpa$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). 3. Parameter constraints (optional) Parameter constraints should be saved in a list. Constraint-list consists of following: constraint$lcpa$equal$big.rho$group (logical) True if param$lcpa$big.rho are constrained to be equal across group variable. Default value = FALSE. constraint$lcpa$equal$big.rho$time (logical) True if param$lcpa$big.rho are constrained to be equal across time points. Default value = FALSE. constraint$lcpa$equal$big.rho$class (logical) True if param$lcpa$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$lcpa$big.rho Integer array of 1 or 0. The elements of constraint$lcpa$big.rho with one represent that the corresponding param$lcpa$big.rho will be freely estimated. The elements of constraint$lcpa$big.rho with 0 means that the corresponding param$lcpa$big.rho will be fixed as zero. Dimension of constraint$lcpa$big.rho is equal to param$lcpa$big.rho. Default setting is to freely estimate. constraint$lcpa$gam.pf Integer array of 1 or 0. The array displays the constraint of param$lcpa$gam.pf. The elements of constraint$lcpa$gam.pf with 1 represents that the corresponding param$lcpa$gam.pf will be freely estimated. The elements of 3

4 constraint$lcpa$gam.pf with 0 means that the corresponding param$lcpa$gam.pf will be fixed as zero. Dimension of constraint$lcpa$gam.pf is npf nc nstr. Default setting is to freely estimate. constraint$lcpa$eta Integer array of 1 or 0. The elements of constraint$lcpa$etaa with 1 represents that the corresponding param$lcpa$eta will be freely estimated. The elements of constraint$lcpa$eta with 0 means that the corresponding param$lcpa$eta will be fixed as zero. Dimension of constraint$lcpa$eta is equal to param$lcpa$eta. 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$lcpa (optional) Starting values provided by users. If starval$is.random = FALSE, then users should provide starting values for LCPA parameters. The dimension starval$param$lcpa is equal to param$lcpa. starval$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 =

5 iteration$eps (optional) Convergence criteria. Default value = 1e-6. 5

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

7 [3,] NA,, 4 [,3] [,4] [1,] [2,] [3,] 2 NA 2 2 ## GAM.PF cvariate of first three subjects LCPA.covariate$gam.pf[1:3,] [1] ## ETA cvariate of first three subjects LCPA.covariate$eta[1:3,,] [,3] [,4] [1,] [2,] [3,] ############### ## LOAD DATA ## ############### data <- list() data$lcpa$si <- LCPA.sItem ########################## ## SPECIFY AN LCPA MODEL ## ########################## model <- list() model$lcpa$is.lcpa <- TRUE model$lcpa$ns <- 3 model$lcpa$npf <- 4 model$lcpa$nrs <- c(2, 2, 2, 2) ############################# 7

8 ## RESTRICT RHO PARAMETERS ## ############################# constraint <- list() constraint$lcpa$equal$big.rho$time <- TRUE ########################## ## STARTING VALUE SETUP ## ########################## starval <- list() starval$is.random <- TRUE ##################### ## RUNNING PROGRAM ## ##################### LCPA.1 <- cat.lvm(data=data, model=model, starval=starval, + constraint=constraint) e e e e-07 OK, converged at 671 summary(lcpa.1) Length Class Mode model 3 -none- list iteration 6 -none- list param 1 -none- list constraint 1 -none- list prior 0 -none- list ######################### ## ESTIMATED PRAMETERS ## ######################### LCPA.1$param $lcpa $lcpa$big.rho,, Stage.1, Time.1,, 8

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

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

11 sitem sitem ,, Stage.2, Time.4,, sitem sitem sitem sitem ,, Stage.3, Time.4,, sitem sitem sitem sitem $lcpa$gam.pf,, Profile Profile Profile Profile $lcpa$eta,, Profile.1,, Time.1 Time.2 Time.3 Time.4 Stage e Stage e Stage e

12 ,, Profile.2,, Time.1 Time.2 Time.3 Time.4 Stage e e Stage e e Stage e e ,, Profile.3,, Time.1 Time.2 Time.3 Time.4 Stage e Stage e Stage e ,, Profile.4,, Time.1 Time.2 Time.3 Time.4 Stage e Stage e Stage e ############################## ## INFO ABOUT EM ITERATIONS ## ############################## LCPA.1$iteration $maxits [1] 2500 $eps [1] 1e-06 $niter [1] 671 $maxdiff 12

13 [1] e-07 $converged [1] TRUE $llvec [1] ################################# ## INFO ABOUT FITTED LCPA MODEL ## ################################# LCPA.1$model $lcpa $lcpa$is.lcpa [1] TRUE $lcpa$npf [1] 4 $lcpa$ns [1] 3 $lcpa$nrs [1] $lcpa$nkase [1] 500 $lcpa$nstr [1] 1 $lcpa$nsi [1] 4 $lcpa$nt [1] 4 13

14 $lcpa$nc [1] 1 $lcpa$ncov $lcpa$ncov$gam.pf [1] 0 $lcpa$ncov$eta [1] 0 $lca $lca$is.lca [1] FALSE $lca$nc [1] 1 $lta $lta$is.lta [1] FALSE ###################################### ## INFO ABOUT PARAMETER CONSTRAINTS ## ###################################### LCPA.1$constraint $lcpa $lcpa$equal $lcpa$equal$big.rho $lcpa$equal$big.rho$group [1] FALSE $lcpa$equal$big.rho$time [1] TRUE 14

15 $lcpa$equal$big.rho$class [1] FALSE $lcpa$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 sitem sitem sitem.4 1 1,, Stage.1, Time.2,, sitem sitem sitem sitem

16 ,, 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,, sitem sitem sitem sitem.4 1 1,, Stage.3, Time.3,, sitem sitem

17 sitem sitem.4 1 1,, Stage.1, Time.4,, sitem sitem sitem sitem.4 1 1,, Stage.2, Time.4,, sitem sitem sitem sitem.4 1 1,, Stage.3, Time.4,, sitem sitem sitem sitem $lcpa$gam.pf,, Profile.1 1 Profile.2 1 Profile.3 1 Profile

18 $lcpa$eta,, Profile.1,, Time.1 Time.2 Time.3 Time.4 Stage Stage Stage ,, Profile.2,, Time.1 Time.2 Time.3 Time.4 Stage Stage Stage ,, Profile.3,, Time.1 Time.2 Time.3 Time.4 Stage Stage Stage ,, Profile.4,, Time.1 Time.2 Time.3 Time.4 Stage Stage Stage ####################################### ## ADD GAM.PF COVARIATES TO THE LCPA ## ####################################### data$lcpa$cov$gam.pf <- LCPA.covariate$gam.pf ##################### ## RUNNING PROGRAM ## 18

19 ##################### LCPA.REG.1.ML <- 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 10 selected. Starting main iteration e e e e-07 OK, converged at 184 #################################### ## ADD ETA COVARIATES TO THE LCPA ## #################################### data$lcpa$cov$eta <- LCPA.covariate$eta ###################################################### ## FIX SOME ETAs AS ZERO TO AVOID BOUNDARY SOLUTION ## ###################################################### constraint$lcpa$eta <- LCPA.REG.1.ML$constraint$lcpa$ETA w <- LCPA.REG.1.ML$param$lcpa$eta <

20 constraint$lcpa$eta[w] <- 0 ########################## ## STARTING VALUE SETUP ## ########################## starval <- list() starval$is.random <- FALSE starval$param <- LCPA.REG.1.ML$param starval$param$lcpa$beta$eta <- + array(0, c(2, LCPA.1$model$lcpa$ns, LCPA.1$model$lcpa$nt, + LCPA.1$model$lcpa$npf, LCPA.1$model$lcpa$nc, + LCPA.1$model$lcpa$nstr)) ##################### ## RUNNING PROGRAM ## ##################### LCPA.REG.2.ML <- cat.lvm(data=data, model=model, starval=starval, + constraint=constraint) Starting main iteration e e e e-07 OK, converged at 620 ######################### ## ESTIMATED PRAMETERS ## ######################### LCPA.REG.2.ML$param $lcpa $lcpa$big.rho,, Stage.1, Time.1,, 20

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

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

23 sitem sitem ,, Stage.2, Time.4,, sitem sitem sitem sitem ,, Stage.3, Time.4,, sitem sitem sitem sitem $lcpa$gam.pf,, Profile Profile Profile Profile $lcpa$eta,, Profile.1,, Time.1 Time.2 Time.3 Time.4 Stage Stage Stage

24 ,, Profile.2,, Time.1 Time.2 Time.3 Time.4 Stage Stage Stage ,, Profile.3,, Time.1 Time.2 Time.3 Time.4 Stage Stage Stage ,, Profile.4,, Time.1 Time.2 Time.3 Time.4 Stage Stage Stage $lcpa$beta $lcpa$beta$gam.pf,,, Profile.1 Profile.2 Profile.3 Profile.4 Int cov.gam.pf $lcpa$beta$eta,, Time.1, Profile.1,, Int NA cov.eta NA 24

25 ,, Time.2, Profile.1,, Int NA cov.eta NA,, Time.3, Profile.1,, Int cov.eta ,, Time.4, Profile.1,, Int NA cov.eta NA,, Time.1, Profile.2,, Int NA cov.eta NA,, Time.2, Profile.2,, Int cov.eta ,, Time.3, Profile.2,, Int. NA 0 NA cov.eta.1 NA 0 NA,, Time.4, Profile.2,, 25

26 Int NA cov.eta NA,, Time.1, Profile.3,, Int. 0 NA cov.eta.1 0 NA ,, Time.2, Profile.3,, Int. 0 NA cov.eta.1 0 NA ,, Time.3, Profile.3,, Int. 0 NA cov.eta.1 0 NA ,, Time.4, Profile.3,, Int. 0 NA cov.eta.1 0 NA ,, Time.1, Profile.4,, Int NA cov.eta NA,, Time.2, Profile.4,, Stage.1 Stage.2 Stage.3 Int NA 26

27 cov.eta NA,, Time.3, Profile.4,, Int. NA NA 0 cov.eta.1 NA NA 0,, Time.4, Profile.4,, Int. NA NA 0 cov.eta.1 NA NA 0 27