=====================================
In this module I give a few basics for working with latent variable model and a complex example from real exprimental data
SEM to build the causal-effect relationships among grographical and climatic variables of genotypic origins and measured functional traits.
A single latent variable acts like a single mising variable. "growth" respresents the overall performance of the species according to all measured functional traits.
Modification indices (MI) were used to detect paths that can be added to the model to improve the goodness of fit.
-
Model fit was evaluated by the comparative fit index (CFI) and Tucker Lewis index (TLI), with values >0.90 and >0.95 indicating a very good model fit.
-
The Chi-Square test (χ2-test) of independence was also used to assess the overall fit of implied theoretical model significantly reproduced the data.
-
As one of the most informative criteria in covariance structure modelling, the value of root mean squared error of approximation (RMSEA) < 0.05 indicates a very good model fit.
-
The 90 % confidence interval (CI) of RMSEA assesses the precision of the RMSEA estimate, and the lower boundary of the CI should contain zero for exact fit.
-
Model fit was also tested by standardized root mean square residual (SRMR), with values < 0.08 indicating a good fit. The 97.5% CIs of coefficient for each path were obtained by bootstrap with 1000 replications.