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Why latent varaibles in SEM do not always work well

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Optimisation of ‘measurement model’ using expected and confirmed SEM links as construct validity constraint.

In structural equation modelling (SEM), the sets of links from latent variables (LVs) to their marker measures are often called ‘the measurement model’, to distinguish them from the regressions linking the construct variables (whether observed or latent), making up ‘the conceptual model’. This distinction can be useful under certain states of theoretical or methodological knowledge, and of availability of variables and data-sources, including applications in psychometrics such as testing between different models for covariance structures (somewhat similar to differing factor analytic solutions). As the embodiment of a theory, SEM provides a good framework for addressing general construct validity of measures. Thus, the main deployment of SEM outside psychometrics is for making medium-to-strong causal inferences from observational (ie non-intervention) data; within this, an LV that assists goodness of fit has to both express both an efficient summary of covariance (like a principal component), and an assertion that the majority of the supposedly causal regressions in and out are similar for all observed variables marking the LV. But this is not always true. This second influence (or requirement for the LV to assist model fit) may or may not assist good measurement of a construct. The ‘measurement model’ in psychometrics can require more traditional and labour-intensive psychometric methods for developing and improving measurement, and showing that the measure is as good as it can reasonably be (eg by Pearson correlations).

We illustrate these points via our use of an adaptive strategy over a period in developing SEMs for two overlapping datasets on children’s middle ear disease and the consequences of this for development and quality of life. We used the first iteration of SEMs as general context for construct validity and worthwhileness of the enterprise. We then returned to a second iteration of measurement (item selection, scaling and weighting) and quantified the improvements achieved. In some instances, the re-scaling of the score-values allocated to items’ response levels improved measurement, as shown by enhanced regression coefficients between variables with already highly significant regression coefficients; in others it left the regression at least no worse, but in revisiting we achieved better handling of missing data. We largely displaced the ‘measurement model’ into prior regressions and principal component analyses with the aim of balancing of validity with reliability and quality of distribution. In the ‘conceptual model’ for causal paths to development and quality of life, LV models were less successful than alternative parallel and serial structures.

This talk is part of the Cambridge Psychometrics Centre Seminars series.

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