### WHAT IS THE STRUCTURAL EQUATION MODEL FRAMEWORK?

SEM is not a single technique, but a general framework that integrates several multivariate techniques into a single model.^{[1] }

SEM is defined as a “path analysis using latent variables.”^{[1] }

Path analysis, or a structural model, is a visual representation of the model, including regression equations between measured variables (see specific notation and example in Figure 1) and a specified causal order.

Latent variables are theoretical constructs that are not directly measured, such as dietary intake.^{[2]}

**Multiple measured variables**can be used to construct a latent variable.- A measured variable is comprised of a true score and error. Error includes systematic error (bias) or random error (equal likelihood of error occurring). By including multiple measured variables, a better measure of the true score and error estimate can be obtained.

**Parameter values**estimate the correlation between the latent variable and the selected measured variable (and its error). Parameter values close to one are highly correlated, and are, therefore, considered to be a good indicator of the latent variable.- For example, to describe childhood dietary intake as a predictor for growth impairment, a parent may be asked to complete a food diary to detail types of foods consumed, calories per meal, and supplemental vitamins consumed. The SEM can test the hypothesized predictor variables documented in the food diary in relation to the unmeasured childhood dietary intake as a latent variable.

SEM provides confirmatory (hypothesis testing) or explanatory (hypothesis generating) analyses.

Confirmatory factor analysis models are imposed on the data and aim to estimate parameters and assess fit of the model to the data.^{[2] }

#### Statistical methods^{[3]}

- The raw data are not incorporated into the model, but rather the variance and covariance of observed data are used to construct a matrix.
- The analysis of the variance/covariance matrix (Figure 2) assesses the model’s ability to summarize the observed matrix.
- Variance (σ2) of each variable with itself (depicted along the diagonal of the matrix) and the covariance between two measured variables make up the cells in the matrix.
- If the implied model is true, then the observed matrix should closely align with the implied model’s matrix values.