This fictional doctoral persistence case demonstrates methodological coaching. It is synthetic evidence, not a client result or validation of the service. Simulation parameters are design targets; every table below uses achieved fitted results.
Case and priority actions
The synthetic sample includes 340 candidates. Before defense, explain the estimand, justify the estimator against the observed measurement scale, and distinguish association from causation. Rehearse uncertainty and limits before discussing model refinement.
Achieved model fit
| Statistic | Value |
|---|---|
| chisq.scaled | 55.083 |
| df.scaled | 60.000 |
| pvalue.scaled | 0.656 |
| cfi.scaled | 1.000 |
| tli.scaled | 1.003 |
| rmsea.scaled | 0.000 |
| rmsea.ci.lower.scaled | 0.000 |
| rmsea.ci.upper.scaled | 0.028 |
| cfi.robust | 1.000 |
| tli.robust | 1.006 |
| rmsea.robust | 0.000 |
| srmr | 0.028 |
| df | 60.000 |
Labels ending in scaled are scaled statistics. Labels ending in robust are robust statistics. They are distinct corrections and must not be substituted for each other. SRMR is reported separately. No ordinal WLSMV sensitivity model was fitted; its fit statistics are unavailable, rather than borrowed from this continuous MLR specification.
Factor specific reliability
| factor | omega | alpha |
|---|---|---|
| A | 0.841 | 0.841 |
| B | 0.867 | 0.866 |
| P | 0.904 | 0.884 |
Composite omega and Cronbach alpha are factor specific. Hierarchical omega is omitted because no general bifactor or second order factor is modeled. Alpha does not establish unidimensionality; missing item covariances also warrant sensitivity checks.
Structural estimates
| Path | Beta | SE_std | B | SE | z | p |
|---|---|---|---|---|---|---|
| A ~ baseline | 0.234 | 0.057 | 0.201 | 0.051 | 3.932 | 0.000 |
| B ~ baseline | 0.139 | 0.055 | 0.107 | 0.044 | 2.468 | 0.014 |
| P ~ A | 0.316 | 0.055 | 0.371 | 0.068 | 5.481 | 0.000 |
| P ~ B | 0.304 | 0.056 | 0.396 | 0.082 | 4.810 | 0.000 |
| P ~ baseline | 0.315 | 0.047 | 0.317 | 0.053 | 6.044 | 0.000 |
The standardized standard errors belong to the standardized estimates. Unstandardized B, SE, z and p appear in separate columns. This observational structural model does not identify causal effects.
Local strain screening
| Indicator1 | Indicator2 | Residual | Residual_z |
|---|---|---|---|
| b1 | a2 | 0.141 | 3.904 |
| Factor | A | B | P |
|---|---|---|---|
| A | 1.000 | 0.399 | 0.511 |
| B | 0.399 | 1.000 | 0.474 |
| P | 0.511 | 0.474 | 1.000 |
Absolute residual correlations above .10, absolute residual z above 2.58, and latent correlations above .85 are contextual screening guides, not rigid pass or fail rules. Revisit wording, theory, and measurement before freeing parameters. Modification indices alone are not a defensible model revision strategy.
Defending missing data assumptions
Committee: How can you defend FIML estimation if you have not proven your data are MAR?
Candidate: MAR cannot generally be distinguished from MNAR using observed data alone. Here the simulation deliberately conditions missingness on observed baseline. In my real study I would justify predictors of missingness, include defensible auxiliary variables, and assess MNAR sensitivity rather than claim MAR is proven. Little’s MCAR test and descriptive comparisons cannot prove MAR. This example includes baseline in the joint model using lavaan FIML with missing = fiml.x and fixed.x = FALSE. Multiple imputation may be preferable when auxiliary structure or the downstream model requires it.
Coaching and boundaries
Prioritize estimator justification and missingness sensitivity, then residual interpretation. Continuous MLR is not automatically appropriate for sparse ordinal items; compare a justified ordinal model when relevant. Explain why a sample of this size does not itself demonstrate sufficient power. Plan model specific Monte Carlo power and precision scenarios. A debrief supports preparation; institutional committee decisions remain outside our control.