Package 'LAWBL' reference manual

Title:	Latent (Variable) Analysis with Bayesian Learning
Description:	A variety of models to analyze latent variables based on Bayesian learning: the partially CFA (Chen, Guo, Zhang, & Pan, 2020) <DOI: 10.1037/met0000293>; generalized PCFA; partially confirmatory IRM (Chen, 2020) <DOI: 10.1007/s11336-020-09724-3>; Bayesian regularized EFA <DOI: 10.1080/10705511.2020.1854763>; Fully and partially EFA.
Authors:	Jinsong Chen [aut, cre, cph]
Maintainer:	Jinsong Chen <[email protected]>
License:	GPL-3
Version:	1.5.2
Built:	2025-02-11 03:26:27 UTC
Source:	https://github.com/jinsong-chen/lawbl

LAWBL: Latent (Variable) Analysis with Bayesian Learning

Description

This package is to provide a variety of models to analyze latent variables based on Bayesian learning.

Details

LAWBL represents a partially confirmatory / exploratory approach to model latent variables based on Bayesian learning. Built on the power of statistical learning, it can address psychometric challenges such as parameter specification, local dependence, and factor extraction. Built on the scalability and flexibility of Bayesian inference and resampling techniques, it can accommodate modeling frameworks such as factor analysis, item response theory, cognitive diagnosis modeling and causal or explanatory modeling. The package can also handle different response formats or a mix of them, with or without missingness. The variety of models provide a partial approach covering a wide range of the exploratory-confirmatory continuum under the context of latent variable modeling.

Towards the confirmatory end, this package includes the Partially Confirmatory Factor Analysis (PCFA) model for continuous data (Chen, Guo, Zhang, & Pan, 2020), the generalized PCFA (GPCFA) model covering continuous, categorical, and mixed-type data, and the partially confirmatory item response model (PCIRM) for continuous and dichotomous data with intercept terms (Chen, 2020). For PCFA, GPCFA, and PCIRM, there are two major model variants with different constraints for identification. One assumes local independence (LI) with a more exploratory tendency, which can be also called the E-step. The other allows local dependence (LD) with a more confirmatory tendency, which can be also called the C-step.

Towards the exploratory end, the Bayesian regularized EFA (BREFA) with factor extraction and parameter estimation in one step (Chen 2021) is offered. It's further improved as the Fully and partially EFA with better performance and partial knowledge.

Parameters are obtained by sampling from the posterior distributions with the Markov chain Monte Carlo (MCMC) techniques. Different Bayesian learning methods are used to regularize the loading pattern, local dependence, and/or factor identification.

Note

This package is under development. You are very welcome to send me any comments or suggestions for improvements, and to share with me any problems you may encounter with the use of this package.

Author(s)

Jinsong Chen, [email protected]

References

Chen, J. (2020). A partially confirmatory approach to the multidimensional item response theory with the Bayesian Lasso. Psychometrika. 85(3), 738-774. DOI:10.1007/s11336-020-09724-3.

Chen, J., Guo, Z., Zhang, L., & Pan, J. (2021). A partially confirmatory approach to scale development with the Bayesian Lasso. Psychological Methods. 26(2), 210-235. DOI: 10.1037/met0000293.

Chen, J. (2021). A generalized partially confirmatory factor analysis framework with mixed Bayesian Lasso methods. Multivariate Behavioral Research. DOI: 10.1080/00273171.2021.1925520.

Chen, J. (2021). A Bayesian regularized approach to exploratory factor analysis in one step. Structural Equation Modeling: A Multidisciplinary Journal. DOI: 10.1080/10705511.2020.1854763.

Chen, J. (2022). Partially confirmatory approach to factor analysis with Bayesian learning: A LAWBL tutorial. Structural Equation Modeling: A Multidisciplinary Journal. DOI: 10.1080/00273171.2021.1925520.

Chen, J. (In Press). Fully and partially exploratory factor analysis with bi-level Bayesian regularization. Behavior Research Methods.

National Longitudinal Survey of Youth 1997

Description

A data set consisted of 3,458 individual responses to 27 mixed-type items, with a 1.12 percentage of missing data

Usage

nlsy27
nlsy27

Format

A list with components:

dat: The response data
Q: Intial design matrix with three factors and two to three specified loadings per factor
cati: Indices of categorical (polytomous) items

(Generalized) Partially Confirmatory Factor Analysis

Description

PCFA is a partially confirmatory approach covering a wide range of the exploratory-confirmatory continuum in factor analytic models (Chen, Guo, Zhang, & Pan, 2021). The PCFA is only for continuous data, while the generalized PCFA (GPCFA; Chen, 2021) covers both continuous and categorical data.

There are two major model variants with different constraints for identification. One assumes local independence (LI) with a more exploratory tendency, which can be also called the E-step. The other allows local dependence (LD) with a more confirmatory tendency, which can be also called the C-step. Parameters are obtained by sampling from the posterior distributions with the Markov chain Monte Carlo (MCMC) techniques. Different Bayesian Lasso methods are used to regularize the loading pattern and LD. The estimation results can be summarized with summary.lawbl and the factorial eigenvalue can be plotted with plot_lawbl.

Usage

pcfa(
  dat,
  Q,
  LD = TRUE,
  cati = NULL,
  cand_thd = 0.2,
  PPMC = FALSE,
  burn = 5000,
  iter = 5000,
  update = 1000,
  missing = NA,
  rfit = TRUE,
  sign_check = FALSE,
  sign_eps = -0.1,
  rs = FALSE,
  auto_stop = FALSE,
  max_conv = 10,
  rseed = 12345,
  digits = 4,
  alas = FALSE,
  verbose = FALSE,
  ort.fac = 0
)
pcfa(
  dat,
  Q,
  LD = TRUE,
  cati = NULL,
  cand_thd = 0.2,
  PPMC = FALSE,
  burn = 5000,
  iter = 5000,
  update = 1000,
  missing = NA,
  rfit = TRUE,
  sign_check = FALSE,
  sign_eps = -0.1,
  rs = FALSE,
  auto_stop = FALSE,
  max_conv = 10,
  rseed = 12345,
  digits = 4,
  alas = FALSE,
  verbose = FALSE,
  ort.fac = 0
)

Arguments

`dat`	A $N \times J$ data matrix or data.frame consisting of the responses of $N$ individuals to $J$ items.
`Q`	A $J \times K$ design matrix for the loading pattern with $K$ factors and $J$ items. Elements are 1, -1, and 0 for specified, unspecified, and zero-fixed loadings, respectively. For models with LI or the E-step, one can specify a few (e.g., 2) loadings per factor. For models with LD or the C-step, the sufficient condition of one specified loading per item is suggested, although there can be a few items without any specified loading. See `Examples`.
`LD`	logical; `TRUE` for allowing LD (model with LD or C-step).
`cati`	The set of categorical (polytomous) items in sequence number (i.e., 1 to $J$ ); `NULL` for no and -1 for all items (default is `NULL`).
`cand_thd`	Candidate parameter for sampling the thresholds with the MH algorithm.
`PPMC`	logical; `TRUE` for conducting posterior predictive model checking.
`burn`	Number of burn-in iterations before posterior sampling.
`iter`	Number of formal iterations for posterior sampling (> 0).
`update`	Number of iterations to update the sampling information.
`missing`	Value for missing data (default is `NA`).
`rfit`	logical; `TRUE` for providing relative fit (DIC, BIC, AIC).
`sign_check`	logical; `TRUE` for checking sign switch of loading vector.
`sign_eps`	minimum value for switch sign of loading vector (if `sign_check=TRUE`).
`rs`	logical; `TRUE` for enabling recommendation system.
`auto_stop`	logical; `TRUE` for enabling auto stop based on `EPSR<1.1`.
`max_conv`	maximum consecutive number of convergence for auto stop.
`rseed`	An integer for the random seed.
`digits`	Number of significant digits to print when printing numeric values.
`alas`	logical; for adaptive Lasso or not. The default is `FALSE`.
`verbose`	logical; to display the sampling information every `update` or not. `Feigen`: Eigenvalue for each factor. `NLA_le3`: Number of Loading estimates >= .3 for each factor. `Shrink`: Shrinkage (or ave. shrinkage for each factor for adaptive Lasso). `EPSR & NCOV`: EPSR for each factor & # of convergence. `Ave. Thd`: Ave. thresholds for polytomous items. `Acc Rate`: Acceptance rate of threshold (MH algorithm). `LD>.2 >.1 LD>.2 >.1`: # of LD terms larger than .2 and .1, and LD's shrinkage parameter. `#Sign_sw`: Number of sign switch for each factor.
`ort.fac`	for orthogonal factors; either scalar 0/1, or a vector of 0/1 with length K.

Value

pcfa returns an object of class lawbl without item intercepts. It contains a lot of information about the posteriors that can be summarized using summary.lawbl.

References

Chen, J., Guo, Z., Zhang, L., & Pan, J. (2021). A partially confirmatory approach to scale development with the Bayesian Lasso. Psychological Methods. 26(2), 210-235. DOI: 10.1037/met0000293.

Chen, J. (2021). A generalized partially confirmatory factor analysis framework with mixed Bayesian Lasso methods. Multivariate Behavioral Research. DOI: 10.1080/00273171.2021.1925520.

Examples


#####################################################
#  Example 1: Estimation with continuous data & LD  #
#####################################################

dat <- sim18cfa1$dat
J <- ncol(dat)
K <- 3
Q<-matrix(-1,J,K);
Q[1:6,1]<-Q[7:12,2]<-Q[13:18,3]<-1

m0 <- pcfa(dat = dat, Q = Q, LD = TRUE,burn = 2000, iter = 2000)
summary(m0) # summarize basic information
summary(m0, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m0, what = 'offpsx') #summarize significant LD terms

######################################################
#  Example 2: Estimation with categorical data & LI  #
######################################################
dat <- sim18ccfa40$dat
J <- ncol(dat)
K <- 3
Q<-matrix(-1,J,K);
Q[1:2,1]<-Q[7:8,2]<-Q[13:14,3]<-1

m1 <- pcfa(dat = dat, Q = Q,LD = FALSE,cati=-1,burn = 2000, iter = 2000)
summary(m1) # summarize basic information
summary(m1, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m1, what = 'offpsx') #summarize significant LD terms
summary(m1,what='thd') #thresholds for categorical items

#####################################################
#  Example 1: Estimation with continuous data & LD  #
#####################################################

dat <- sim18cfa1$dat
J <- ncol(dat)
K <- 3
Q<-matrix(-1,J,K);
Q[1:6,1]<-Q[7:12,2]<-Q[13:18,3]<-1

m0 <- pcfa(dat = dat, Q = Q, LD = TRUE,burn = 2000, iter = 2000)
summary(m0) # summarize basic information
summary(m0, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m0, what = 'offpsx') #summarize significant LD terms

######################################################
#  Example 2: Estimation with categorical data & LI  #
######################################################
dat <- sim18ccfa40$dat
J <- ncol(dat)
K <- 3
Q<-matrix(-1,J,K);
Q[1:2,1]<-Q[7:8,2]<-Q[13:14,3]<-1

m1 <- pcfa(dat = dat, Q = Q,LD = FALSE,cati=-1,burn = 2000, iter = 2000)
summary(m1) # summarize basic information
summary(m1, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m1, what = 'offpsx') #summarize significant LD terms
summary(m1,what='thd') #thresholds for categorical items

Partially Confirmatory Item Response Model

Description

pcirm is a partially confirmatory approach to item response models (Chen, 2020), which estimates the intercept for continuous and dichotomous data. Similar to PCFA and GPCFA, there are two major model variants with different constraints for identification. One assumes local independence (LI) with a more exploratory tendency, which can be also called the E-step. The other allows local dependence (LD) with a more confirmatory tendency, which can be also called the C-step. Parameters are obtained by sampling from the posterior distributions with the Markov chain Monte Carlo (MCMC) techniques. Different Bayesian Lasso methods are used to regularize the loading pattern and LD. The estimation results can be summarized with summary.lawbl and the factorial eigenvalue can be plotted with plot_lawbl.

Usage

pcirm(
  dat,
  Q,
  LD = TRUE,
  cati = NULL,
  PPMC = FALSE,
  burn = 5000,
  iter = 5000,
  update = 1000,
  missing = NA,
  rseed = 12345,
  sign_check = FALSE,
  sign_eps = -0.5,
  auto_stop = FALSE,
  max_conv = 10,
  digits = 4,
  alas = FALSE,
  verbose = FALSE
)
pcirm(
  dat,
  Q,
  LD = TRUE,
  cati = NULL,
  PPMC = FALSE,
  burn = 5000,
  iter = 5000,
  update = 1000,
  missing = NA,
  rseed = 12345,
  sign_check = FALSE,
  sign_eps = -0.5,
  auto_stop = FALSE,
  max_conv = 10,
  digits = 4,
  alas = FALSE,
  verbose = FALSE
)

Arguments

`dat`	A $N \times J$ data matrix or data.frame consisting of the responses of $N$ individuals to $J$ items. Only continuous and dichotomous data are supported.
`Q`	A $J \times K$ design matrix for the loading pattern with $K$ factors and $J$ items. Elements are 1, -1, and 0 for specified, unspecified, and zero-fixed loadings, respectively. For models with LI or the E-step, one can specify a few (e.g., 2) loadings per factor. For models with LD or the C-step, the sufficient condition of one specified loading per item is suggested, although there can be a few items without any specified loading. See `Examples`.
`LD`	logical; `TRUE` for allowing LD (model with LD or C-step).
`cati`	The set of dichotomous items in sequence number (i.e., 1 to $J$ ); `NULL` for no and -1 for all items (default is `NULL`).
`PPMC`	logical; `TRUE` for conducting posterior predictive model checking.
`burn`	Number of burn-in iterations before posterior sampling.
`iter`	Number of formal iterations for posterior sampling (> 0).
`update`	Number of iterations to update the sampling information.
`missing`	Value for missing data (default is `NA`).
`rseed`	An integer for the random seed.
`sign_check`	logical; `TRUE` for checking sign switch of loading vector.
`sign_eps`	minimum value for switch sign of loading vector (if `sign_check=TRUE`).
`auto_stop`	logical; `TRUE` for enabling auto stop based on `EPSR<1.1`.
`max_conv`	maximum consecutive number of convergence for auto stop.
`digits`	Number of significant digits to print when printing numeric values.
`alas`	logical; for adaptive Lasso or not. The default is `FALSE`.
`verbose`	logical; to display the sampling information every `update` or not. `Feigen`: Eigenvalue for each factor. `NLA_le3`: Number of Loading estimates >= .3 for each factor. `Shrink`: Shrinkage (or ave. shrinkage for each factor for adaptive Lasso). `EPSR & NCOV`: EPSR for each factor & # of convergence. `Ave. Int.`: Ave. item intercept. `LD>.2 >.1 LD>.2 >.1`: # of LD terms larger than .2 and .1, and LD's shrinkage parameter. `#Sign_sw`: Number of sign switch for each factor.

Value

pcirm returns an object of class lawbl with item intercepts. It contains a lot of information about the posteriors that can be summarized using summary.lawbl.

References

Chen, J. (2020). A partially confirmatory approach to the multidimensional item response theory with the Bayesian Lasso. Psychometrika. 85(3), 738-774. DOI:10.1007/s11336-020-09724-3.

Examples


####################################
#  Example 1: Estimation with LD   #
####################################

dat <- sim24ccfa21$dat
J <- ncol(dat)
K <- 3
Q<-matrix(-1,J,K);
Q[1:8,1]<-Q[9:16,2]<-Q[17:24,3]<-1

m0 <- pcirm(dat = dat, Q = Q, LD = TRUE, cati = -1, burn = 2000,iter = 2000)
summary(m0) # summarize basic information
summary(m0, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m0, what = 'offpsx') #summarize significant LD terms

####################################
#  Example 2: Estimation with LD   #
####################################

Q<-cbind(Q,-1);
Q[15:16,4]<-1

m1 <- pcirm(dat = dat, Q = Q, LD = FALSE, cati = -1, burn = 2000,iter = 2000)
summary(m1) # summarize basic information
summary(m1, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m1, what = 'offpsx') #summarize significant LD terms

####################################
#  Example 1: Estimation with LD   #
####################################

dat <- sim24ccfa21$dat
J <- ncol(dat)
K <- 3
Q<-matrix(-1,J,K);
Q[1:8,1]<-Q[9:16,2]<-Q[17:24,3]<-1

m0 <- pcirm(dat = dat, Q = Q, LD = TRUE, cati = -1, burn = 2000,iter = 2000)
summary(m0) # summarize basic information
summary(m0, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m0, what = 'offpsx') #summarize significant LD terms

####################################
#  Example 2: Estimation with LD   #
####################################

Q<-cbind(Q,-1);
Q[15:16,4]<-1

m1 <- pcirm(dat = dat, Q = Q, LD = FALSE, cati = -1, burn = 2000,iter = 2000)
summary(m1) # summarize basic information
summary(m1, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m1, what = 'offpsx') #summarize significant LD terms

Partially Exploratory Factor Analysis

Description

PEFA is a partially exploratory approach to factor analysis, which can incorporate partial knowledge together with unknown number of factors, using bi-level Bayesian regularization. When partial knowledge is not needed, it reduces to the fully exploratory factor analysis (FEFA; Chen, 2021). A large number of factors can be imposed for selection where true factors will be identified against spurious factors. The loading vector is reparameterized to tackle model sparsity at the factor and loading levels with the multivariate spike and slab priors. Parameters are obtained by sampling from the posterior distributions with the Markov chain Monte Carlo (MCMC) techniques. The estimation results can be summarized with summary.lawbl and the trace or density of the posterior can be plotted with plot_lawbl.

Usage

pefa(
  dat,
  Q = NULL,
  K = 8,
  mjf = 3,
  PPMC = FALSE,
  burn = 5000,
  iter = 5000,
  missing = NA,
  eig_eps = 1,
  sign_eps = 0,
  rfit = TRUE,
  rs = FALSE,
  update = 1000,
  rseed = 12345,
  verbose = FALSE,
  auto_stop = FALSE,
  max_conv = 10,
  digits = 4
)
pefa(
  dat,
  Q = NULL,
  K = 8,
  mjf = 3,
  PPMC = FALSE,
  burn = 5000,
  iter = 5000,
  missing = NA,
  eig_eps = 1,
  sign_eps = 0,
  rfit = TRUE,
  rs = FALSE,
  update = 1000,
  rseed = 12345,
  verbose = FALSE,
  auto_stop = FALSE,
  max_conv = 10,
  digits = 4
)

Arguments

`dat`	A $N \times J$ data matrix or data.frame consisting of the responses of $N$ individuals to $J$ items.
`Q`	A $J \times K$ design matrix for the loading pattern with $K$ factors and $J$ items for `PEFA`. Elements are 1, -1, and 0 for specified, unspecified, and zero-fixed loadings, respectively. It's not needed for `FEFA`, which is the default. See `Examples`.
`K`	Maximum number of factors for selection under `FEFA`. Not used for `PEFA`.
`mjf`	Minimum number of items per factor.
`PPMC`	logical; `TRUE` for conducting posterior predictive model checking.
`burn`	Number of burn-in iterations before posterior sampling.
`iter`	Number of formal iterations for posterior sampling (> 0).
`missing`	Value for missing data (default is `NA`).
`eig_eps`	minimum eigenvalue for factor extraction.
`sign_eps`	minimum value for switch sign of loading vector.
`rfit`	logical; `TRUE` for providing relative fit (DIC, BIC, AIC).
`rs`	logical; `TRUE` for enabling recommendation system.
`update`	Number of iterations to update the sampling information.
`rseed`	An integer for the random seed.
`verbose`	logical; to display the sampling information every `update` or not. `Feigen`: Eigenvalue for each factor. `NLA_lg0`: Number of Loading magnitudes > 0 for each factor. `iShrink`: Inverted shrinkage parameter for each factor. `True Fa`: Is the factor identified as true or not. `EPSR & NCOV`: EPSR for each factor & # of convergence. `ROW: LA overflow,sign switch,bk=0, <eig_eps`: Loading overflow, sign switch, vector bk=0 and eigenvalue<eig_eps.
`auto_stop`	logical; `TRUE` for enabling auto stop based on EPSR.
`max_conv`	maximum consecutive number of convergence for auto stop.
`digits`	Number of significant digits to print when printing numeric values.

Value

pcfa returns an object of class lawbl without item intercepts. It contains a lot of information about the posteriors that can be summarized using summary.lawbl.

References

Chen, J. (2021). A Bayesian regularized approach to exploratory factor analysis in one step. Structural Equation Modeling: A Multidisciplinary Journal, 28(4), 518-528. DOI: 10.1080/10705511.2020.1854763.

Chen, J. (In Press). Fully and partially exploratory factor analysis with bi-level Bayesian regularization. Behavior Research Methods.

Examples


#####################################################
#  Example 1: Fully EFA                             #
#####################################################

dat <- sim18cfa0$dat

m0 <- pefa(dat = dat, K=5, burn = 2000, iter = 2000,verbose = TRUE)
summary(m0) # summarize basic information
summary(m0, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m0, what = 'phi') #summarize factorial correlations
summary(m0, what = 'eigen') #summarize factorial eigenvalue

##########################################################
#  Example 2: PEFA with two factors partially specified  #
##########################################################

J <- ncol(dat)
K <- 5
Q<-matrix(-1,J,K);
Q[1:2,1]<-Q[7:8,2]<-1
Q

m1 <- pefa(dat = dat, Q = Q,burn = 2000, iter = 2000,verbose = TRUE)
summary(m1)
summary(m1, what = 'qlambda')
summary(m1, what = 'phi')
summary(m1,what='eigen')

#####################################################
#  Example 1: Fully EFA                             #
#####################################################

dat <- sim18cfa0$dat

m0 <- pefa(dat = dat, K=5, burn = 2000, iter = 2000,verbose = TRUE)
summary(m0) # summarize basic information
summary(m0, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m0, what = 'phi') #summarize factorial correlations
summary(m0, what = 'eigen') #summarize factorial eigenvalue

##########################################################
#  Example 2: PEFA with two factors partially specified  #
##########################################################

J <- ncol(dat)
K <- 5
Q<-matrix(-1,J,K);
Q[1:2,1]<-Q[7:8,2]<-1
Q

m1 <- pefa(dat = dat, Q = Q,burn = 2000, iter = 2000,verbose = TRUE)
summary(m1)
summary(m1, what = 'qlambda')
summary(m1, what = 'phi')
summary(m1,what='eigen')

Posterior plots for `lawbl` object

Description

Provide posterior plots based on the factorial eigenvalues of a lawbl object. For PEFA or FEFA, only true factors will be plotted.

Usage

plot_lawbl(object, what = "trace", istart = 1, iend = -1)
plot_lawbl(object, what = "trace", istart = 1, iend = -1)

Arguments

`object`	A `lawbl` object
`what`	A list of options for what to plot. `trace`: The trace of each factor's eigenvalue. `density`: The trace of each factor's eigenvalue. `EPSR`: Estimated Potential Scale Reduction (Gelman-Rubin diagnostics) for each factor.
`istart`	Starting point of the Markov chain for plotting.
`iend`	Ending point of the Markov chain for plotting; -1 for the actual final point.

Examples


dat <- sim18cfa0$dat
J <- ncol(dat)
K <- 3
Q<-matrix(-1,J,K);
Q[1:2,1]<-Q[7:8,2]<-Q[13:14,3]<-1


m0 <- pcfa(dat = dat, Q = Q, LD = FALSE,burn = 1000, iter = 1000)
plot_lawbl(m0) # trace
plot_lawbl(m0, what='density')
plot_lawbl(m0, what='EPSR')

dat <- sim18cfa0$dat
J <- ncol(dat)
K <- 3
Q<-matrix(-1,J,K);
Q[1:2,1]<-Q[7:8,2]<-Q[13:14,3]<-1


m0 <- pcfa(dat = dat, Q = Q, LD = FALSE,burn = 1000, iter = 1000)
plot_lawbl(m0) # trace
plot_lawbl(m0, what='density')
plot_lawbl(m0, what='EPSR')

Simulating data with Latent Variable Modeling

Description

sim_lvm can simulate data with continuous latent variables (factors) and continuous or categorical observed variables, plus a MIMIC-type structure. One can also include an error covariance (local dependence) structure. Categorical observed variables are generated with latent continuous responses normally distributed and equally spaced within [-3,3].

Usage

sim_lvm(
  N = 1000,
  lam = 0.7,
  K = 3,
  J = 18,
  cpf = 0,
  lac = 0.3,
  phi = 0.3,
  ecr = 0,
  necw = K,
  necb = K,
  P = 0,
  phix = 0,
  b = 0,
  lam1 = 0,
  K1 = 0,
  J1 = 0,
  b1 = 0,
  phi1 = 0,
  ilvl = NULL,
  cati = NULL,
  noc = c(4),
  misp = 0,
  fac_score = FALSE,
  rseed = 333,
  digits = 4
)
sim_lvm(
  N = 1000,
  lam = 0.7,
  K = 3,
  J = 18,
  cpf = 0,
  lac = 0.3,
  phi = 0.3,
  ecr = 0,
  necw = K,
  necb = K,
  P = 0,
  phix = 0,
  b = 0,
  lam1 = 0,
  K1 = 0,
  J1 = 0,
  b1 = 0,
  phi1 = 0,
  ilvl = NULL,
  cati = NULL,
  noc = c(4),
  misp = 0,
  fac_score = FALSE,
  rseed = 333,
  digits = 4
)

Arguments

`N`	Sample size.
`lam`	Loading value (for major loadings) or matrix ( $J \times K$ ).
`K`	Number of factors (if `lam` is a value).
`J`	Number of items (if `lam` is a value).
`cpf`	Number of cross-loadings per factor (if `lam` is a value).
`lac`	Cross-loading value (if `lam` is a value).
`phi`	Factor correlation scalar or matrix, or error correlations (for MIMIC-type model).
`ecr`	Error covariance (local dependence) value.
`necw`	Number of within-factor local dependence.
`necb`	Number of between-factor local dependence.
`P`	Number of observable predictors (for MIMIC-type model).
`phix`	Observable predictor correlation value or matrix (for MIMIC-type model).
`b`	Coefficients of observable predictors (for MIMIC-type model), value or $K \times P$ .
`lam1`	Loading value (for major loadings) or matrix ( $J1 \times K1$ ) for latent predictors (for MIMIC-type model).
`K1`	Number of latent predictors (if `lam` is a value, for MIMIC-type model).
`J1`	Number of items latent predictors (if `lam` is a value, for MIMIC-type model).
`b1`	Coefficients of latent predictors (for MIMIC-type model), value or $K \times K1$
`phi1`	Latent predictor correlation scalar or matrix (for MIMIC-type model).
`ilvl`	Specified levels of all items (i.e., need to specify Item 1 to $J+P+J1$ ); Any value smaller than 2 is considered as continuous item.
`cati`	The set of polytomous items in sequence number (i.e., can be any number set in between 1 and $J+P$ ); `NULL` for no and -1 for all (if `ilvl=NULL`).
`noc`	Number of levels for polytomous items.
`misp`	Proportion of missingness.
`fac_score`	Output factor score or not.
`rseed`	An integer for the random seed.
`digits`	Number of significant digits to print when printing numeric values.

Value

An object of class list containing the data, loadings, factor correlations, local dependence, and other information. The data consists of J items for the factors, P items for observable predictors, and J1 items for latent predictors.

Examples


# for continuous data with cross-loadings and local dependence effect .3
out <- sim_lvm(N=1000,K=3,J=18,lam = .7, lac=.3,ecr=.3)
summary(out$dat)
out$lam
out$loc_dep

# for categorical data with cross-loadings .4 and 10% missingness
out <- sim_lvm(N=1000,K=3,J=18,lam = .7, lac=.4,cati=-1,noc=4,misp=.1)
summary(out$dat)
out$lam
out$loc_dep

# for continuous data with cross-loadings and local dependence effect .3
out <- sim_lvm(N=1000,K=3,J=18,lam = .7, lac=.3,ecr=.3)
summary(out$dat)
out$lam
out$loc_dep

# for categorical data with cross-loadings .4 and 10% missingness
out <- sim_lvm(N=1000,K=3,J=18,lam = .7, lac=.4,cati=-1,noc=4,misp=.1)
summary(out$dat)
out$lam
out$loc_dep

Simulated CCFA data with LI and missingness

Description

Categorical CFA data simulated based on 18 items, 3 factors, and 4 categories with local independence and 10 percent missingness at random; factorial correlation $\Phi=.3$ .

Usage

sim18ccfa40
sim18ccfa40

Format

A list with components:

dat: A dataset with simulated responses of 1000 individuals to 18 items
qlam: Loading pattern and values used to simulated the data

Simulated CCFA data with LD and missingness

Description

Categorical CFA data simulated based on 18 items, 3 factors, and 4 categories with local dependence and 10 percent missingness at random; factorial correlation $\Phi=.3$ .

Usage

sim18ccfa41
sim18ccfa41

Format

A list with components:

dat: A dataset with simulated responses of 1000 individuals to 18 items
qlam: Loading pattern and values used to simulated the data
LD: Local dependence between items (LD effect = .3)

Simulated CFA data with LI

Description

CFA data simulated based on 18 items, 3 factors and local independence; factorial correlation $\Phi=.3$ .

Usage

sim18cfa0
sim18cfa0

Format

A list with components:

dat: A dataset with simulated responses of 1000 individuals to 18 items
qlam: Loading pattern and values used to simulated the data

Simulated CFA data with LD

Description

CFA data simulated based on 18 items, 3 factors and local dependence; factorial correlation $\Phi=.3$ .

Usage

sim18cfa1
sim18cfa1

Format

A list with components:

dat: A dataset with simulated responses of 1000 individuals to 18 items
qlam: Loading pattern and values used to simulated the data
LD: Local dependence between items (LD effect = .3)

Simulated MCFA data with LD and Missingness

Description

CFA data mixed with continuous and categorical responses simulated based on 3 factors, 6 4-category items, 12 continuous items, local dependence, and 10 percent missigness at random; factorial correlation $\Phi=.3$ .

Usage

sim18mcfa41
sim18mcfa41

Format

A list with components:

dat: A dataset with simulated responses of 1000 individuals to 18 items
qlam: Loading pattern and values used to simulated the data
LD: Local dependence between items (LD effect = .3)

Simulated CCFA data (dichotomous) with LD and a minor factor/trait

Description

Categorical CFA data simulated based on 24 items, 4 factors, 2 categories and local dependence; factorial correlation $\Phi=.3$ . The last factor/trait is minor (measured by cross-loadings only).

Usage

sim24ccfa21
sim24ccfa21

Format

A list with components:

dat: A dataset with simulated responses of 1000 individuals to 24 items
qlam: Loading pattern and values used to simulated the data
LD: Local dependence between items (LD effect = .3)

Summary method for `lawbl` objects

Description

Provide summaries of posterior information for a lawbl object, .

Usage

## S3 method for class 'lawbl'
summary(
  object,
  what = "basic",
  med = FALSE,
  SL = 0.05,
  detail = FALSE,
  digits = 4,
  istart = 1,
  iend = -1,
  ...
)
## S3 method for class 'lawbl'
summary(
  object,
  what = "basic",
  med = FALSE,
  SL = 0.05,
  detail = FALSE,
  digits = 4,
  istart = 1,
  iend = -1,
  ...
)

Arguments

`object`	A `lawbl` object
`what`	A list of options for what to summarize. `basic`: Basic information about the model and posteriors. `lambda`: Loading estimates. `qlambda`: Loading estimates in pattern/Q-matrix format. `eigen`: Factorial eigen value. `dpsx`: Diagonal elements in the residual covariance matrix `PSX`. `offpsx`: Off-diagonal elements in `PSX`; local dependence terms. `phi`: Factorial correlations. `thd`: Threshold estimates. `int`: Intercept estimates (for `pcirm` only). `shrink`: (Ave) shrinkage for each factor's loadings and LD (if `LD` in `pcfa` = T). `factor`: Are the factors true of not (for EFA). `all`: All above information.
`med`	logical; if the posterior median (`TRUE`) or mean (`FALSE`) is used as the estimate.
`SL`	Significance level for interval estimate. The default is .05.
`detail`	logical; if only significant (`FALSE`) or all (`TRUE`) estimates are presented.
`digits`	Number of significant digits to print when printing numeric values.
`istart`	Starting point of the Markov chain for summary.
`iend`	Ending point of the Markov chain for summary; -1 for the actual final point.
`...`	additional arguments

Value

A list or matrix containing the summarized information based on the option what.

Examples


dat <- sim18cfa0$dat
J <- ncol(dat)
K <- 3
Q<-matrix(-1,J,K);
Q[1:2,1]<-Q[7:8,2]<-Q[13:14,3]<-1

m0 <- pcfa(dat = dat, Q = Q, LD = FALSE,burn = 1000, iter = 1000)
summary(m0) # summarize basic information
summary(m0, what = 'lambda') #summarize significant loadings
summary(m0, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m0, what = 'offpsx') #summarize significant LD terms

dat <- sim18cfa0$dat
J <- ncol(dat)
K <- 3
Q<-matrix(-1,J,K);
Q[1:2,1]<-Q[7:8,2]<-Q[13:14,3]<-1

m0 <- pcfa(dat = dat, Q = Q, LD = FALSE,burn = 1000, iter = 1000)
summary(m0) # summarize basic information
summary(m0, what = 'lambda') #summarize significant loadings
summary(m0, what = 'qlambda') #summarize significant loadings in pattern/Q-matrix format
summary(m0, what = 'offpsx') #summarize significant LD terms

Package 'LAWBL'

Help Index

LAWBL: Latent (Variable) Analysis with Bayesian Learning

Description

Details

Note

Author(s)

References

National Longitudinal Survey of Youth 1997

Description

Usage

Format

(Generalized) Partially Confirmatory Factor Analysis

Description

Usage

Arguments

Value

References

Examples

Partially Confirmatory Item Response Model

Description

Usage

Arguments

Value

References

Examples

Partially Exploratory Factor Analysis

Description

Usage

Arguments

Value

References

Examples

Posterior plots for lawbl object

Description

Usage

Arguments

Examples

Simulating data with Latent Variable Modeling

Description

Usage

Arguments

Value

Examples

Simulated CCFA data with LI and missingness

Description

Usage

Format

Simulated CCFA data with LD and missingness

Description

Usage

Format

Simulated CFA data with LI

Description

Usage

Format

Simulated CFA data with LD

Description

Usage

Format

Simulated MCFA data with LD and Missingness

Description

Usage

Format

Simulated CCFA data (dichotomous) with LD and a minor factor/trait

Description

Usage

Format

Summary method for lawbl objects

Description

Usage

Arguments

Value

Examples

Posterior plots for `lawbl` object

Summary method for `lawbl` objects