User:LesHayduk/sandbox

 Testing models [edit]

It is important to test whether a model is consistent with the available data. A model containing estimated coefficients implies a specific covariance matrix among the observed indicator variables. This model-implied covariance matrix can be tested for consistency with the actual data covariances using χ2 if the estimates were obtained by maximum likelihood. Current best practice requires reporting the model χ2, its degrees of freedom, and probability. Models significantly inconsistent with the data require improvement. The diversity of models and variety of potential misspecifications preclude stereotypical corrective responses and instead encourage thorough diagnostic assessment of: potential data mistakes, model programming errors, problematic estimation, incorrect effect directions, insufficient latent variables, and mistakes in connecting the latent variables to the indicators. Research areas following path-analytic traditions tended to respect model testing while areas grounded in factor analysis tended to disregard testing by switching from model testing to covariance-fit indexing. For example, it is possible for factor models to perfectly fit data produced by non-factor worldly causal structures. Given that seriously misspecified models may perfectly correspond to the data, even small inconsistencies between a model and the data may constitute the first detectable sign of important model deficiencies. Consequently it is incorrect to claim that small amounts of ill fit signal only minor model deficiencies. The possibility of minimal ill fit signaling major model misspecification renders dubious the selection of models based on fit indices, and recommends caution if coefficients are inserted to improve model fit because this may constitute bandaging a dead model.