Supplemental Digital Content 2. Text - Resource page with information regarding LTA general
procedure.
This document contains a brief outline of some of the general considerations when conducting
LTA. This is not an exhaustive review of the procedure and more detailed information can be found in the
references, from which this information was obtained, listed at the end of this document.
Steps in LTA procedure
Step 1: Study measurement model alternatives for each time point
Purpose: To assure the appropriate measurement model one needs to select the correct
number of classes for the latent class model.
How to do it: Models with various numbers of classes, and at each time point, can be
constructed and compared for best fit, parsimony, and interpretability or congruence with theory. Most
often a two class model is constructed first and successive numbers of classes are added. Fit can be
assessed in several ways including likelihood ratio tests and use of information criteria statistics such as
the AIC and BIC. After the number of classes is determined, classes can be labeled based on data
patterns and theory. See SDC 3 for Mplus syntax for setting up latent class models.
Cautions: The overall structure of the latent classes can change over time (e.g. there are only
two classes at time one but four classes at time two). This phenomenon would indicate a lack of
measurement invariance and can make interpretation of results difficult. Measurement invariance can
be assessed in step 2.
Step 2: Explore transitions based on cross-sectional results (not shown in paper)
Purpose: This preliminary step is done for at least two reasons, 1) to describe change in class
membership over time to get an indication of the amount and type of movement occurring in the data
and 2) to conduct measurement invariance tests to determine whether the meaning of the classes stays
the same over time.
How to do it: Crosstabs of most likely membership are calculated across time points. Most likely
membership is drawn from the latent class analysis results. Measurement invariance can be tested by
comparing models with differing levels of constraints (allowing items response probabilities to be freely
estimated across groups versus setting them to be equal across groups) and determining the best fit
based on log likelihood ratio tests.
Cautions: In times where full measurement invariance does not hold, careful interpretation of
results is required. In cases where item response probabilities are different across groups but the
general pattern formed is the same, the investigator must make a determination about whether it is
appropriate to compare latent class prevalences.
Step 3: Explore specification of the latent transition model without covariates (not shown in paper)
Purpose: This step may involve a stepwise approach to setting up a full longitudinal model.
Models with several time points and/or several manifest items may take a long time to run. It is
sometimes helpful to start with just two time points and work toward the full model. During this setup
of the full model, two things can be explored – higher order effects and transition stability. Higher order
effects are those which demonstrate the lasting effects of class membership over time. For example, if
the analysis in the paper included three time points, the effect of being in the High Barriers class at time
3 could be related to membership in that class at time 1 not just time 2. In this step, it may also be
important to determine whether the transitions across time should be stationary and/or restricted in
some way. Stationary transitions are those that are set to be the same across time. Restricted
transitions are those such as the Longitudinal Guttman Simplex wherein a certain order to class
membership exists and the transitions are fixed so that individuals cannot move backward in class
membership. A common example of this is math skill acquisition. Children cannot learn to subtract or
multiply before they learn to add and once they learn these skills, they generally do not lose the skills. In
this case, transitions would be restricted in such a way that children are only allowed to move forward in
their skill acquisition rather than backward and forward.
How to do it: Higher order effects can be tested by relating future time points to earlier time
points rather than just the most proximal time point. Syntax is written to allow, for example, time 3 to
be related both directly to time 1 and indirectly to time 1 through time 2. Transition restrictions can be
set in many ways. For example, to set transitions to be equal across time in Mplus, the same numbers
are assigned in parenthesis after each item that is to be set equal.
Cautions: The possibilities for setting higher order effects and transition restrictions are
numerous and are not all listed here. It is important that decisions about these types of model
specifications are guided by theory. In addition, when covariates are added to the model, setting
transitions to be stationary is no longer meaningful. This is because current class membership would be
estimated based on not just previous class membership but also the covariates. However, the previous
class membership dummy variable is the same across time points when stationarity is imposed so any
important differences would bias the estimation of the covariate coefficients.
Step 4: Include covariates in the LTA model
Purpose: Covariates can be added to help explain latent class membership at any point in time.
How to do it: Covariates are added into the model as predictors of class membership. See SDC 4
for Mplus syntax for adding covariates to the model.
Cautions: As above, there are numerous possibilities for adding covariates to the model
including, to name a few, those that are time varying (such as levels of depression), time invariant (such
as demographics), and latent (such as the mover stayer model described below). Decisions should be
guided by theory.
Step 5: Include distal outcomes and advanced modeling extensions
Purpose: Distal outcomes can be related to class membership in order to understand the
influence class membership has on an outcome at a point later in time. Modeling extensions can be
included to further explain or understand the change process. These extensions may include modeling
subpopulations within the sample. A common example is the mover stayer model wherein some
individuals transition over time and other individuals do not. Another example, shown in the paper,
involves subpopulations of individuals in groups created by the study design, intervention and control.
How to do it: Distal outcomes are added to the model as variables within a class that can be
freely estimated and then tested. See SDC 5 for Mplus syntax for adding distal outcomes to the model.
Some modeling extensions to consider include estimating a full model with a compilation of higher
order effects, transition restrictions, covariates and distal outcomes. In addition, modeling
subpopulations in the sample made be done here. Adding known or unknown subpopulations to the
model can be complicated. Depending on the model that might be appropriate, different steps are
required and typically include setting of start values and parameter restrictions. See SDC 6 for Mplus
syntax for LTA with known groups.
Cautions: Adding distal outcomes can be done in a variety of ways. Again, one should base
decisions on theory. With modeling extensions such as compiling a variety of effects, very large sample
sizes are often required. With the case of modeling subpopulations, another possible issue of concern is
label switching. Label switching can occur in latent class and latent transition analysis, but is particularly
an issue with modeling extensions such as the mover/stayer model or treatment/control model when
one wants to compare classes across these groups. Label switching can occur because the order of
latent classes is determined arbitrarily by the software based on starting values. Label switching is an
event wherein class 1 is labeled by the software as class 1 for one group and class 1 is labeled by the
software as class 2 for the other group. For example in the paper, the High Barriers class was labeled
class 1 for the treatment group but it was labeled as class 2 in the control group. This was discovered by
exploring the match between response patterns for each variable and the class assignments in the
CPROB output. When label switching occurs, the solution may still be accurate, but the interpretation
must be carefully made, particularly when determining if there is a difference in transition probabilities
across groups. Label switching can often be avoided by assigning carefully determined start values. See
SDC 6 for Mplus syntax on assigning start values.
Useful references
Detailed and comprehensive information on LTA procedure
Collins, L. M., & Lanza, S. T. (2010). Latent Class and Latent Transition Analysis. Wiley: New Jersey.
Nylund, K. (2007). Latent transition analysis: Modeling extensions and an application to peer
victimization. Doctoral dissertation, University of California, Los Angeles.
General information on LTA with substantive examples
Collins, L. M., Graham, J. W., Scarborough Rousculp, S., Fidler P. L., Pan, J., & Hansen, W. B. (1994).
Latent transition analysis and how it can address prevention research questions. In L. M. Collins
& L. A. Seitz (Eds.), Advances in Data Analysis for Prevention Intervention Research (National
Institute of Drug Abuse Monograph 142).
Guo, J., Collins, L. M., Hill, K. G., Hawkins, J. D. (2000). Developmental pathways to alcohol abuse and
dependence in young adulthood. Journal of Studies on Alcohol, 799-808.
Humphreys, K. & Jansen, H. (2000). Latent transition analysis with covariates, nonresponse, summary
statistics, and diagnostics: Modeling children’s drawing development. Multivariate Behavioral
Research, 35 (1), 89-118.
Kaplan, D. (2008). An overview of Markov chain methods for the study of stage-sequential
developmental processes. Developmental Psychology, 44, 457-467.
Lanza, S. T., Patrick, M. E., Maggs, J. L. (2010). Latent transition analysis: Benefits of a latent variable
approach to modeling transitions in substance use. Journal of Drug Issues, 40(1), 93-120.
Reuter, M., Hennig, J., Netta, P., Buehner, M., & Hueppe, M. (2004). Using Latent Mixed Markov Models
for the choice of the best pharmacological treatment. Statistics in Medicine, 23, 1337-1349.
The Mplus website also lists several papers at http://www.statmodel.com/papers.shtml
List of software that can be used to conduct LTA
Mplus
SAS – using proc LCA and proc LTA
LatentGold
ℓEM