lta: Latent transition analysis

In latents: Multilevel Latent Profile, Class and Transition Models

Latent transition analysis

Description

Fits latent profiles to repeated observations of the same group and estimates the probabilities of moving between them from one occasion to the next. The measurement model is that of multilpa() – Gaussian, categorical or mixed indicators, invariant across occasions – so profiles keep the same meaning at every occasion and a change of profile is a change of state rather than a change of definition. With more than one group class, each class carries its own initial distribution and its own transition matrix, which is how groups that differ in their dynamics are separated from groups that differ only in where they start.

Usage

lta(
  data,
  vars,
  id,
  n_profiles,
  time,
  n_group_classes = 1L,
  variance_model = c("varying", "equal"),
  n_starts = 10L,
  max_iter = 1000L,
  tol = 1e-08,
  min_variance = 1e-06,
  seed = NULL,
  missing = c("error", "fiml"),
  covariance_model = c("diagonal", "full"),
  categorical = character(),
  min_probability = 1e-10,
  occasions = c("observed", "grid"),
  select_start = c("likelihood", "converged"),
  transitions = c("homogeneous", "occasion"),
  transition_covariates = character(),
  initial_covariates = character(),
  measurement = c("invariant", "occasion"),
  order = 1L,
  model = NULL,
  mover_stayer = FALSE,
  weights = NULL,
  ordinal = character(),
  count = character(),
  count_model = c("poisson", "negative_binomial"),
  count_dispersion = c("varying", "equal")
)

Arguments

data	A data frame containing indicators and a group identifier.
vars	Unique character vector of continuous indicator column names.
id	Name of the observed group identifier column. Character, factor, or numeric identifiers are supported; missing identifiers are not. Required here: this model has a second level by construction, so it has no single-level form and does not take multilpa()'s id = NULL.
n_profiles	Integer number of individual profiles, at least two.
time	Name of the column giving each observation's occasion within its group. Required: this model is defined by the ordering. Values must be complete and unique within each group.
n_group_classes	Positive integer number of latent group classes. One gives an ordinary single-level latent transition model; more than one fits a mixture of transition models over groups.
variance_model	Either "varying" (profile-specific variances or covariance matrices) or "equal" (shared across profiles).
n_starts	Positive integer number of EM starts. The first is deterministic: Ward's hierarchical clustering of the standardized indicators (on at most 2000 evenly spaced rows), each cluster described by its own means and spread, which is the start mclust's name refers to and finds solutions whose profiles differ in shape. The rest are k-means from random centres. When start is supplied, it supplies the first start instead; remaining starts are random initializations. It is ignored when max_iter = 0 and start is supplied: that call evaluates the supplied parameters and nothing else, so exactly one start is run whatever n_starts says.
max_iter	Nonnegative integer maximum number of EM updates per start. max_iter = 0 performs no update. With start, it returns the model evaluated at exactly those values, whatever n_starts is, so that logLik() scores a parameter set supplied from elsewhere rather than the best of some random initializations that were never asked for. Without start there is nothing to evaluate at, so the random initializations are scored and the highest is returned.
tol	Positive relative log-likelihood tolerance. Convergence requires absolute change no greater than ⁠tol * (1 + abs(previous log likelihood))⁠.
min_variance	Positive lower bound on each variance, or each covariance eigenvalue for full covariance, in squared input units. This defines a constrained maximum-likelihood problem. Bound-active estimates are explicitly reported and generate a warning.
seed	Optional random seed: any whole number set.seed() accepts, negative ones included. With a supplied seed, the caller's random-number state is restored on exit.
missing	"error" rejects missing indicators; "fiml" maximizes the observed-data likelihood under an ignorable missingness mechanism (MAR). Missing indicators are integrated out, not filled in for likelihood fitting. This holds with membership covariates too; the covariates themselves must be complete (latents_bad_data).
covariance_model	"diagonal" assumes conditional independence; "full" estimates within-profile residual covariances.
categorical	Character vector naming indicators to treat as categorical. Each is modelled by unrestricted, profile-specific response probabilities over its observed categories, which is the latent class measurement model. Binary, ordinal and unordered indicators are all handled by the same unrestricted parameterization; numeric, integer, logical, character and factor columns are accepted. Indicators not named here stay Gaussian, so naming a subset fits a mixed-mode model.
min_probability	Positive lower bound on every categorical response probability, defining a constrained maximum-likelihood problem in the same way min_variance does for Gaussian indicators.
occasions	How a group's occasions are placed on the transition grid. "observed" numbers each group's own observations consecutively, so a transition always links two adjacent observations. "grid" places them on the grid of every position seen in the data, so a group that skips a position still consumes a transition across the gap and contributes no measurement information at it. The two agree whenever every group is observed at every position.
select_start	Which start the fit reports. "likelihood", the default, takes the highest log likelihood across starts, preferring a converged start only among those tied with it to within a relative 1e-10. "converged" takes the highest log likelihood among the converged starts whenever at least one converged, and falls back to every start when none did. Use it when an unconverged start edges out a converged one by a negligible amount, which happens when a membership logit creeps along a flat ridge of the likelihood: the converged start is then a maximum that the standard errors can work with, and the other is not. summary() and get_results(fit, "starts") show every start either way.
transitions	"homogeneous" (the default) uses one transition matrix for every occasion; "occasion" estimates a separate one for each move (occasion 1 to 2, 2 to 3, ...).
transition_covariates	Names of columns whose values shift the transition probabilities through a multinomial logit per origin profile: the log odds of moving to each other profile rather than staying. A column may change over occasions; the value at the destination occasion is used. Factors are expanded to indicator columns.
initial_covariates	Names of columns that shift the initial profile distribution (a multinomial logit, reference: the last profile), read at each group's first occasion.
measurement	"invariant" (the default) keeps the profiles' means, variances and response probabilities equal across occasions; "occasion" estimates them separately at each occasion, so a profile is defined by its position in the sequence of transitions rather than by one fixed measurement model.
order	1 (the default) or 2. With 2, the profile at each occasion from the third on depends on the profiles at the two previous occasions (a second-order Markov chain); the first move stays first order.
model	A covariance structure as multilpa() takes it ("EEI", "VVI", "VEI", ... ; mclust's codes). Standard errors are given for EEI, VVI, EEE and VVV in the homogeneous model and for the diagonal EEI and VVI with the extensions; other structures are refused (latents_unsupported_inference).
mover_stayer	TRUE adds a class of stayers: groups that never change profile (identity transitions) and have their own initial profile distribution (Goodman's mover-stayer model). n_group_classes then counts the mover classes; the stayer class is reported as "stayers".
weights	NULL, or the name of a column of data holding one sampling weight per id (constant over its occasions). As in multilpa(): pseudo maximum likelihood with the weights scaled to sum to the number of id units, sandwich standard errors by default, and integer weights equal to repeating each sequence. A weighted fit uses the general transition engine and returns a multilpa_lta.
ordinal, count, count_model, count_dispersion	Ordinal and count indicators, as in multilpa(); with measurement = "occasion" their parameters are estimated per occasion. Read them with get_results(fit, "ordinal") and get_results(fit, "count_means"). A fit with them uses the general transition engine.

Details

This is latent transition analysis (LTA); with more than one group class it is a mixture over transition patterns, so the classes are trajectories rather than states. multilpa() is the cross-sectional counterpart.

By default transitions are first order and homogeneous over occasions: the probability of moving from one profile to another does not depend on the occasion or on earlier profiles. Measurement parameters are shared across occasions and across group classes. A profile that no group occupies before its final occasion leaves its transition row without information; the row is then uniform by construction rather than estimated. Such a row is warned about when the model is fitted, is flagged by the estimated column of the transition table and is listed by get_results(fit, "transitions", estimated = FALSE). Profile labels are arbitrary and are not comparable across fits without alignment.

max_iter = 0 updates nothing: the starting values are evaluated and returned with the expectation they imply, and the fit reports converged = FALSE after zero iterations. Every reported quantity, including expected_count and the implied profile prevalence, is then read off that single expectation.

Value

A multilpa_transitions object containing means, variances, optional covariances and response_probabilities, initial_probabilities (group classes by profiles), transition_probabilities (profiles by profiles by group classes, rows indexing the profile moved from), group_probabilities, posterior matrices, classifications, log likelihood, information criteria, restart diagnostics and convergence history. Use get_results() for the tidy transition table and for the other tables. No standard errors, likelihood-ratio tests or guarantees of global optimality are given for this model family.

With transitions = "occasion", transition_covariates, initial_covariates, measurement = "occasion" or order = 2 the result is a multilpa_lta object instead, read with get_results.multilpa_lta(): transition and initial logit coefficients with Wald standard errors (observed, robust or OPG, from analytic scores), model-implied transition probabilities per occasion, profiles per occasion. Missing indicators (missing = "fiml") and covariance structures are supported; diagonal fits are finished by a quasi-Newton search on the exact likelihood, others by EM. Agreement with Mplus (User's Guide examples 8.13, 8.14; occasion-specific thresholds), depmixS4 and LMest is recorded in ⁠equivalence/lta-extensions/⁠ of the source repository.

References

Collins, L. M., & Lanza, S. T. (2010). Latent class and latent transition analysis. Wiley.

Vermunt, J. K. (2003). Multilevel latent class models. Sociological Methodology, 33, 213–239. doi:10.1111/j.0081-1750.2003.t01-1-00131.x.

See Also

get_results() for the fitted transition probabilities and for the assignments in order, and multilpa() for the cross-sectional model this one shares its measurement parameters with.

Examples

# Students take their courses in their own order, which `sequence` records,
# so the same enrolments that fit a cross-sectional model fit a transition
# one. Engagement mostly persists from one course to the next.
fit <- lta(
  course_engagement,
  vars = c("browse", "lectures", "forum_read", "forum_post", "attendance"),
  id = "student", n_profiles = 2, time = "sequence", n_starts = 2, seed = 1
)
get_results(fit, what = "transitions")
summary(fit)

latents documentation built on Oct. 16, 2026, 5:09 p.m.