Table 1.
Overview of the Trajectory Modelling Techniques
| Latent Class modelling approaches | Cluster Analysis | Sequence Analysis | ||||
|---|---|---|---|---|---|---|
| GMM | GBTM | LTA | LCA | |||
| Statistical technique | Parametric finite mixture model; Allows heterogeneity within subgroups |
Semi-parametric finite mixture model; Do not allow heterogeneity within subgroups | Semi-parametric finite mixture model | Semi-parametric finite mixture model | Nonparametric approach | Nonparametric approach |
| Rationale of use | Statistical modelling of repeated measures of a given variable | Modelling of a variable at one point in time | Modelling of a variable at one point in time | Modelling of sequences of states or events that unfold over a period of time | ||
| Possibility to include covariates | yes | yes | Yes | yes | yes | yes |
| Study design | Longitudinal | Longitudinal | Longitudinal | Cross-sectional | Cross-sectional | Longitudinal |
| Type of variables | Continuous; Categorical (nominal or ordinal) |
Continuous; Categorical (nominal or ordinal) | Categorical (nominal or ordinal) |
Categorical | Continuous; Categorical (nominal or ordinal); Mixed |
Categorical (sequential) |
| Type of distributions | Normal; Binary; Censored; normal; Poisson; Zero-inflated Poisson | Binary; Censored normal; Poisson; Zero-inflated Poisson | Binary; Multinomial | Binary; Multinomial | N/A | N/A |
| Methodological choices to be made | Class-membership probability thresholds Number of classes/trajectories in the study population/Indicators: Bayesian Information Criterion (BIC), Clinical judgment, Parsimony, Minimum acceptable % of patients in each class |
Algorithm to be used | States to be prioritized when multiple states occur simultaneously | |||
| Available statistical software programs | lcmm R-package; Mplus | SAS Proc traj; CrimCV R-package; Mplus; traj Stata-plugin | SAS Proc lta; poLCA and depmixs4 R-package, Mpus | SAS Proc LCA; poLCA and depmixs4R-package; Mplus, Others | SAS Proc cluster; R; SPSS Cluster analysis; Stata Cluster and Clustermat; Others | SAS, TraMineR R-package |
| Examples of applications (variables) | Clinical symptoms (eg, pain intensity or interference); Developmental trajectories; Acculturative changes; Perceived racial discrimination; Self-Esteem; Behaviours | Clinical symptoms (eg, pain intensity or interference); Quality of life; Healthcare visits; Body mass; Developmental trajectories of physical aggression | Alcohol use; Sexual behaviours; Racial identity; Adolescents’ beliefs about parental authority | Behaviours (eg, alcohol, substances, sexual, behavioural obesity risk factors) | Clinical symptoms (eg, pain interference, depression); Healthcare visits; Expectations | Healthcare visits |
| Examples of studies reporting the use of the approach | 12,42,45,48,132 | 11,26,27,30,62,133,134 | 68,135-138 | 85,87,90 | 103–105 | 18,51,115-117,124 |
Notes: R: A language and environment for statistical computing (R Core Team, Vienna, Austria); Mplus: Mplus Computer Software (Muthén & Muthén, Los Angeles, CA, USA); SAS: SAS software (SAS Institute, Cary, NC, USA); Stata: Stata Statistical Software (StataCorp LLC., College Station, TX, USA); SPSS: IBM SPSS Statistics for Windows (IBM Corp., Armonk, NY, US).
Abbreviations: GMM, growth mixture modelling; GBTM, group-based trajectory modelling; LTA, latent transition analysis; LCA, latent class analysis.