This is the family of models that models a dynamic factor model on panel data. All functions accept both wide-format data (with a design matrix for vars) and long-format data (with a character vector for vars plus idvar and optionally beepvar). The format is auto-detected from the type of vars. There are four covariance structures that can be modeled in different ways: within_latent, between_latent for the within-person and between-person latent (contemporaneous) models respectively, and within_residual, between_residual for the within-person and between-person residual models respectively. The panellvgvar wrapper automatically models all latent networks as GGMs. The old name panel_lvgvar is deprecated in favor of panellvgvar. dlvm() is the primary short name of dlvm1() (identical function; the historical "1" referred to the lag order). The observed-variable special case of this family (a factor loading matrix fixed to identity and zero residual variances) is the panel VAR model, implemented as its own faster framework in panelvar and panelgvar. The mean structure is stationary by default (item intercepts nu invariant across waves, latent means fixed to zero); stationary_means = FALSE makes the intercepts wave-specific, giving the trend-stationary case (see the details below).
dlvm1(data, vars, datatype = c("auto", "wide", "long"),
idvar, beepvar,
standardize = c("none", "z", "quantile", "z_per_wave"),
lambda, within_latent = c("cov", "chol",
"prec", "ggm", "cor"), within_residual = c("cov", "chol",
"prec", "ggm", "cor"), between_latent = c("cov", "chol",
"prec", "ggm", "cor"), between_residual = c("cov", "chol",
"prec", "ggm", "cor"), beta = "full", omega_zeta_within =
"full", delta_zeta_within = "diag", kappa_zeta_within
= "full", sigma_zeta_within = "full",
lowertri_zeta_within = "full", omega_epsilon_within =
"zero", delta_epsilon_within = "diag",
kappa_epsilon_within = "diag", sigma_epsilon_within =
"diag", lowertri_epsilon_within = "diag",
omega_zeta_between = "full", delta_zeta_between =
"diag", kappa_zeta_between = "full",
sigma_zeta_between = "full", lowertri_zeta_between =
"full", omega_epsilon_between = "zero",
delta_epsilon_between = "diag", kappa_epsilon_between
= "diag", sigma_epsilon_between = "diag",
lowertri_epsilon_between = "diag", nu, mu_eta,
identify = TRUE, identification = c("loadings",
"variance"), latents, groups, groupvar, covs,
cors, means, nobs, corinput, start
= "version2", covtype = c("choose", "ML", "UB"),
missing = "auto", equal = "none",
baseline_saturated = TRUE, estimator = "ML",
optimizer, storedata = FALSE, verbose = FALSE,
sampleStats, baseline =
c("stationary_random_intercept", "stationary",
"independence", "none"), bootstrap = FALSE, boot_sub,
boot_resample, within, between,
penalty_lambda = NA, penalty_alpha = 1,
penalize_matrices,
rho_zeta_within = "full", SD_zeta_within = "diag",
rho_epsilon_within = "zero", SD_epsilon_within = "diag",
rho_zeta_between = "full", SD_zeta_between = "diag",
rho_epsilon_between = "zero", SD_epsilon_between = "diag",
beta_epsilon = "zero",
temporal_latent = c("raw","PDC"),
temporal_residual = c("raw","PDC"),
PDC = "full", PDC_epsilon = "zero",
stationary_means = TRUE)dlvm(...)
panellvgvar(...)
panel_lvgvar(...)
An object of the class psychonetrics (psychonetrics-class)
A data frame encoding the data used in the analysis. Can be missing if covs and nobs are supplied.
Required argument. For wide-format data, this must be a *matrix* with each row indicating a variable and each column indicating a measurement. The matrix must be filled with names of the variables in the dataset corresponding to variable i at wave j. NAs can be used to indicate missing waves. The rownames of this matrix will be used as variable names. For long-format data, this should be a character vector of variable names in the dataset.
Data format: "auto" (default) auto-detects based on whether vars is a matrix (wide) or character vector (long). "wide" forces wide-format interpretation. "long" forces long-format interpretation with automatic reshape to wide.
Optional string indicating the subject/cluster ID variable in data. Required when datatype = "long" or when vars is a character vector.
Optional string indicating the time point / measurement occasion variable. If missing when datatype = "long", a sequential measurement variable is created per subject.
Standardization method: "none" (default), "z" for global z-scores per variable across all waves (uses the overall mean and standard deviation for each variable computed across all waves of data), "quantile" for quantile normalization across all waves, "z_per_wave" for independent z-scores per wave column (note: this imposes stationarity as means become 0 and variances become 1 at each wave).
Required argument. A model matrix encoding the factor loading structure. Each row indicates an indicator and each column a latent. A 0 encodes a fixed to zero element, a 1 encoding a free to estimate element, and higher integers encoding equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
The type of within-person latent contemporaneous model to be used.
The type of within-person residual model to be used.
The type of between-person latent model to be used.
The type of between-person residual model to be used.
A model matrix encoding the temporal relationships (transpose of temporal network). A 0 encodes a fixed to zero element, a 1 encoding a free to estimate element, and higher integers encoding equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix. Can also be "full" for a full temporal network or "zero" for an empty temporal network.
Only used when within_latent = "ggm". Can be "full", "zero", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when within_latent = "ggm". Can be "diag", "zero" (not recommended), or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when within_latent = "prec". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when within_latent = "cov". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when within_latent = "chol". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when within_residual = "ggm". Can be "full", "zero", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when within_residual = "ggm". Can be "diag", "zero" (not recommended), or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when within_residual = "prec". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when within_residual = "cov". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when within_residual = "chol". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when between_latent = "ggm". Can be "full", "zero", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when between_latent = "ggm". Can be "diag", "zero" (not recommended), or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when between_latent = "prec". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when between_latent = "cov". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when between_latent = "chol". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when between_residual = "ggm". Can be "full", "zero", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when between_residual = "ggm". Can be "diag", "zero" (not recommended), or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when between_residual = "prec". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when between_residual = "cov". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Only used when between_residual = "chol". Can be "full", "diag", or a typical model matrix with 0s indicating parameters constrained to zero, 1s indicating free parameters, and higher integers indicating equality constraints. For multiple groups, this argument can be a list or array with each element/slice encoding such a matrix.
Optional vector encoding the intercepts of the observed variables. Set elements to 0 to indicate fixed to zero constrains, 1 to indicate free intercepts, and higher integers to indicate equality constraints. For multiple groups, this argument can be a list or array with each element/column encoding such a vector. When stationary_means = FALSE this is instead a nVar by nTime matrix (variables in the rows, waves in the columns), or an array/list of such matrices for multiple groups; elements at variable--wave combinations that are not in the vars design matrix are always fixed to zero.
Optional vector encoding the means of the latent variables. Set elements to 0 to indicate fixed to zero constrains, 1 to indicate free intercepts, and higher integers to indicate equality constraints. For multiple groups, this argument can be a list or array with each element/column encoding such a vector. The latent means are fixed to zero by identify() for identification, with a stationary as well as with a wave-specific mean structure.
Logical, should the model be automatically identified?
Type of identification used. "loadings" to fix the first factor loadings to 1, and "variance" to fix the diagonal of the latent variable model matrix (sigma_zeta, lowertri_zeta, delta_zeta or kappa_zeta) to 1.
An optional character vector with names of the latent variables.
Deprecated. Use groupvar instead. An optional string indicating the name of the group variable in data.
An optional string indicating the name of the group variable in data. Replaces the deprecated groups argument; if both are supplied, groupvar takes precedence with a warning.
A sample variance--covariance matrix, or a list/array of such matrices for multiple groups. Make sure the covtype argument is set correctly to the type of covariances used.
A sample correlation matrix, or a list/array of such matrices for multiple groups. When supplied, the matrix is treated as a covariance matrix with a warning (appropriate for standardized data). Requires nobs. Note: corinput = TRUE is not supported in dlvm1.
A vector of sample means, or a list/matrix containing such vectors for multiple groups. This argument always refers to the sample means; the mean structure of the model is set with stationary_means.
The number of observations used in covs and means, or a vector of such numbers of observations for multiple groups.
Logical. Not supported in dlvm1() and will produce an error if set to TRUE.
Start value specification. Can be either a string or a psychonetrics model. If it is a string, "version2" indicates the latest version of start value computation, "version1" indicates start values as they were computed up to version 0.11, and "simple" indicate simple starting values. If this is a psychonetrics model the starting values will be based on the output. This can be useful, for example, if you first estimate a model with matrices set to a Cholesky decomposition, then use those values as start values for estimating Gaussian graphical models.
How should missingness be handled in computing the sample covariances and number of observations when data is used. Can be "auto" (default) for automatic detection, "listwise" for listwise deletion, or "pairwise" for pairwise deletion. When "auto", the function checks for missing data and switches ML to FIML, PML to PFIML, or defaults to listwise for LS estimators.
A character vector indicating which matrices should be constrained equal across groups.
A logical indicating if the baseline and saturated model should be included. Mostly used internally and NOT Recommended to be used manually.
The estimator to be used. Currently implemented are "ML" for maximum likelihood estimation, "FIML" for full-information maximum likelihood estimation, "PML" for penalized maximum likelihood estimation, "PFIML" for penalized full-information maximum likelihood estimation, "ULS" for unweighted least squares estimation, "WLS" for weighted least squares estimation, and "DWLS" for diagonally weighted least squares estimation. When missing = "auto" (default), "ML" is automatically switched to "FIML" and "PML" to "PFIML" if missing data is detected.
The optimizer to be used. Can be one of "nlminb" (the default R nlminb function), "ucminf" (from the optimr package), "nloptr_TNEWTON" (preconditioned truncated Newton via nloptr), and "LBFGS++" (pure C++ L-BFGS-B). Defaults to "nlminb".
Logical, should the raw data be stored? Needed for bootstrapping (see bootstrap).
Logical, should progress be printed to the console?
An optional sample statistics object. Mostly used internally.
If 'covs' is used, this is the type of covariance (maximum likelihood or unbiased) the input covariance matrix represents. Set to "ML" for maximum likelihood estimates (denominator n) and "UB" to unbiased estimates (denominator n-1). The default will try to find the type used, by investigating which is most likely to result from integer valued datasets.
What baseline model should be used? "stationary_random_intercept" includes both within- and between person variances constrained equal across time (default), "stationary" only includes within-person variances constrained equal across time, "independence" (default up to version 0.11) includes a variance for every variable at every time point (not constrained equal across time), and "none" includes no baseline model. The baseline model always uses the same mean structure as the model itself (see the stationary_means argument and the details below).
Should the data be bootstrapped? If TRUE the data are resampled and a bootstrap sample is created. These must be aggregated using aggregate_bootstraps! Can be TRUE or FALSE. Can also be "nonparametric" (which sets boot_sub = 1 and boot_resample = TRUE) or "case" (which sets boot_sub = 0.75 and boot_resample = FALSE).
Proportion of cases to be subsampled (round(boot_sub * N)).
Logical, should the bootstrap be with replacement (TRUE) or without replacement (FALSE)
Optional alias for within_latent. If both within and within_latent are explicitly specified, within_latent takes precedence and a warning is issued.
Optional alias for between_latent. If both between and between_latent are explicitly specified, between_latent takes precedence and a warning is issued.
Numeric penalty strength for penalized ML estimation (PML/PFIML). NA (default) triggers automatic selection via EBIC-based grid search when a penalized estimator is used; set to a specific numeric value to use a fixed penalty strength (0 = no penalty). See find_penalized_lambda and penalize.
Elastic net mixing parameter: 1 = LASSO (default), 0 = ridge.
Character vector of matrix names to penalize. If missing, defaults are selected based on the model type.
Only used when within_latent = "cor". Correlation matrix specification ("full", "zero", or a pattern matrix; see omega_zeta_within).
Only used when within_latent = "cor". Diagonal standard-deviation matrix specification ("diag", "full", or a pattern matrix; see delta_zeta_within).
Only used when within_residual = "cor". Correlation matrix specification ("zero", "full", or a pattern matrix).
Only used when within_residual = "cor". Diagonal standard-deviation matrix specification ("diag", "full", or a pattern matrix).
Only used when between_latent = "cor". Correlation matrix specification ("full", "zero", or a pattern matrix).
Only used when between_latent = "cor". Diagonal standard-deviation matrix specification ("diag", "full", or a pattern matrix).
Only used when between_residual = "cor". Correlation matrix specification ("zero", "full", or a pattern matrix).
Only used when between_residual = "cor". Diagonal standard-deviation matrix specification ("diag", "full", or a pattern matrix).
Residual (within-person) temporal effects: a model matrix for the lag-1 autoregression of the residuals, epsilon_t = beta_epsilon epsilon_(t-1) + u_t. "zero" (default) gives white-noise residuals (the model as it was before this argument existed). "diag" gives each indicator its own residual autoregression, which models item-specific carry-over (autocorrelated uniquenesses) with a geometrically decaying structure; "full" or a pattern matrix are also allowed. When beta_epsilon is non-zero, sigma_epsilon_within (and its typed variants) parameterizes the innovation covariance of the residual process, and the stationary residual covariance is available as the "sigma_epsilon_within_stationary" matrix in getmatrix. At least three waves are required for a non-zero beta_epsilon to be identified, and at least four are recommended (the residual autoregression, the stable between-person residual variance in sigma_epsilon_between, and the latent dynamics compete for the same lagged covariance information).
Parameterization of the latent temporal effects: "raw" (default) models beta directly; "PDC" models the latent partial directed correlations directly, with the PDC matrix encoding from = row and to = column (the transposed orientation relative to beta). A (pattern-constrained) PDC model is fit-equivalent to the corresponding raw model, but standard errors, confidence intervals, equality constraints and modification indices then apply directly on the PDC scale.
Parameterization of the residual temporal effects (beta_epsilon): "raw" (default) or "PDC" (models the residual partial directed correlations PDC_epsilon, standardized with respect to the residual innovation covariance, directly).
Only used when temporal_latent = "PDC". Model matrix for the latent partial directed correlations (from = row, to = column): "full", "zero", "diag", or a pattern matrix.
Only used when temporal_residual = "PDC". Model matrix for the residual partial directed correlations (from = row, to = column): "zero" (default), "diag", "full", or a pattern matrix.
Logical. TRUE (default, and the behavior of all earlier versions) has item intercepts nu that are invariant across waves and latent means fixed to zero, so that the implied means are equal across waves. FALSE makes the item intercepts wave-specific (the nu matrix becomes nVar by nTime), which saturates the mean structure and adds nVar * (nTime - 1) parameters; the latent means stay fixed to zero. See the details below.
Arguments sent to dlvm1.
Sacha Epskamp
Stationary versus wave-specific means. By default the model is fully stationary in the means: the item intercepts nu are invariant across waves and the latent means are fixed to zero, so the implied means are equal at every wave. With stationary_means = FALSE the item intercepts become wave-specific, \(\mu_t = \nu_t + \Lambda \alpha\) with \(\alpha = 0\). This is the classical trend-stationary case: the level shifts are period effects exogenous to the dynamics, the within-person latent deviation process remains covariance-stationary, and wave 1 is still drawn from that stationary distribution. The implied covariance matrix is therefore identical to that of the stationary-means model; only the mean part of the model (and of its Jacobian) changes.
Identification. The latent means (mu_eta) are fixed to zero with a stationary as well as with a wave-specific mean structure, and the wave-specific intercepts are free: one per variable--wave combination present in the vars design matrix (variable--wave combinations that are absent have no intercept parameter). Wave-specific intercepts and wave-specific latent means are not jointly identified, so one of the two has to carry the level shifts. Placing them in the intercepts saturates the mean structure, which is what keeps the baseline model (an observed-variable panelvar model, which cannot have latent means) nested in the fitted model, so that incremental fit indices remain interpretable. The estimated intercepts then equal the observed per-wave means, and the likelihood-ratio test of stationary_means = TRUE against FALSE is a test of equal means over time with nVar * (nTime - 1) degrees of freedom. The flip side is that a saturated mean structure cannot separate period effects on the constructs from mean-level measurement drift (scalar non-invariance), and cannot be tested for misfit: nu absorbs both. Users who want the more restrictive alternative (invariant intercepts with free latent means at waves 2 and later, nLat(nTime - 1) parameters, testable when nLat < nVar) can specify it manually with the nu and mu_eta arguments plus identify = FALSE, keeping in mind that the baseline model is then no longer nested in the fitted model. In the degenerate observed-variable case (lambda the identity matrix with zero residual variances) the model with stationary_means = FALSE is identical to panelvar with stationary_means = FALSE, with nu playing the role of mu.
No free innovation variances. Only the means can be freed over time, not the innovation (co)variances: a wave-varying innovation covariance has no stationary distribution for wave 1 to be drawn from, so the stationarity machinery on which this family is built does not apply. Wave-specific innovation structures are covered by the RI-CLPM / RI-CLPN framework instead, see ri_clpm.
Baseline model. The baseline model always uses the same mean structure as the fitted model: with stationary_means = FALSE the baseline (a panelvar model with empty networks) gets wave-specific means as well, so that both models have exactly the same (saturated) mean structure. A baseline model must be nested in the fitted model, otherwise it can fit better than the fitted model on the mean side (a free-means baseline against an equal-means target would beat it), which makes incremental fit indices meaningless or negative. A corollary is that incremental fit indices (CFI, TLI, NFI, ...) are not directly comparable between a stationary_means = TRUE and a stationary_means = FALSE fit of the same data, because the two use different baselines by design; compare those two models with a likelihood-ratio test (compare) instead. The saturated model already has a saturated mean structure and is unchanged.
panelvar for the observed-variable (panel VAR) special case of this family.
library("dplyr")
# Smoke data cov matrix, based on LISS data panel https://www.dataarchive.lissdata.nl
smoke <- structure(c(47.2361758611759, 43.5366809116809, 41.0057465682466,
43.5366809116809, 57.9789886039886, 47.6992521367521,
41.0057465682466,
47.6992521367521, 53.0669434731935), dim = c(3L, 3L),
dimnames = list(
c("smoke2008", "smoke2009", "smoke2010"), c("smoke2008",
"smoke2009", "smoke2010")))
# Design matrix:
design <- matrix(rownames(smoke),1,3)
# Form dlvm1 model with a single latent variable per wave:
mod <- dlvm1(vars = design, lambda = matrix(1),
covs = smoke, nobs = 352
)
# \donttest{
# Run model:
mod <- mod %>% runmodel
# Evaluate fit:
mod %>% fit
# }
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