Modifying a structural equation model of child dietary intake using the Lagrange Multiplier test in SAS® PROC CALIS for MWSUG 2014

Structural equation models (SEM) allow for simultaneous evaluation of causal pathways between multiple predictors and outcomes, including latent variables, given a hypothesized theoretical model. If an initial SEM does not meet appropriate fit criteria, model modification can achieved through utilization of statistical results from the Lagrange Multiplier (LM) test and theoretical knowledge. To demonstrate modification of a SEM, baseline data from a garden-based nutrition intervention with elementary school children were examined using SAS® PROC CALIS. The two outcome variables of interest are fruit and vegetable intake (individually). Several measured determinants are hypothesized to predict these practices, including two latent variables, willingness to try fruit and vegetables, which have six indicator variables each. Initial model fit was not acceptable (χ 2 : 407.9, 111 df, p<0.0001; RMSEA: 0.09, CFI: 0.89). From the LM statistic we identified several unaccounted for correlations between errors on indicators of willingness to try fruits and vegetables. These correlations are theoretically sensible given that items on these scales are worded identically, save for the words “fruit” and “vegetable”, and these modifications were made. Once correlations between comparable indicators were added to the SEM, model fit was improved (χ 2 : 234.0, 105 df, p<0.0001; RMSEA: 0.06, CFI: 0.95). Additional relationships identified by the LM test were evaluated, but none were theoretically meaningful, and the second model was accepted as final. Use of the LM test in PROC CALIS facilitates theoretically appropriate modification of an a priori SEM in order to improve overall model fit and produce more reliable parameter estimates.