Introductory And Intermediate Growth Models - Mplus

Growth Model Estimation, Testing, AndModel Modification• Estimation: Model parameters– Maximum-likelihood (ML) estimation under normality– ML and non-normality robust s.e.’s– Quasi-ML (MUML): clustered data (multilevel)– WLS: categorical outcomes– ML-EM: missing data, mixtures• Model Testing– Likelihood-ratio chi-square testing; robust chi square– Root mean square of approximation (RMSEA):Close fit (≤ .05)• Model Modification– Expected drop in chi-square, EPC• Estimation: Individual growth factor values (factor scores)– Regression method – Bayes modal – Empirical Bayes– Factor determinacy55CFA Modeling Estimation And TestingEstimatorsIn CFA, a covariance matrix and a mean vector are analyzed.• ML – minimizes the differences between matrix summaries(determinant and trace) of observed and estimatedvariances/covariances• Robust ML – same estimates as ML, standard errors and chisquarerobust to non-normality of outcomes and nonindependenceof observations (MLM, MLR)Chi-square test of model fitTests that the model does not fit significantly worsethan a model where the variables correlate freely – p-valuesgreater than or equal to .05 indicate good fitH 0 : Factor modelH 1 : Free variance-covariance modelIf p < .05, H 0 is rejectedNote: We want large p5628