Path Analysis and Structural Equation Model (SEM)

More questions that SEM can answer:

5) What are the parameter estimates from the model? 6) Are there any indirect or mediating effects in the model? 7) Are there group differences? 8) Can change in the variance (or mean) be tracked over time?

Yet more questions that SEM can answer:

9) Can a model be estimated with individual and group level components 10) Can latent categorical variables be estimated? 11) Can a latent group membership be estimated from continuous and discrete variables? 12) Can we predict the rate at which people will drop out of a study or end treatment?

What is the biggest problem with Chi-square Goodness-of-Fit?

Requires a very large sample size

Is SEM an exploratory or confirmatory approach? Why?

SEM is a confirmatory approach because we need to have established theory about the relationships. SEM is not causal.

Structural Equation Model (SEM) vs. Path Analysis - which one is better to analysis a mediation effect? Why?

SEM is better because of the problems that a path analysis may have.

Other limitations of SEM that can be dealt with

5) Missing data 6) Multivariate normality 7) Linearity 8) No multicollinearity/singularity 9) Residuals covariance*

Residuals covariance(s) in SEM

Covariance observed in sample - covariance implied by the model We want it small, centered around zero, and symmetric distribution of errors.

Structural model

- concerns about causal linkages among variables - relates variables or factors to one another - variables can be underlying constructs (as generated from the measurement model) or measurable variables

Measurement model

- generate a construct (latent) by extracting from a range of observable (measurable) variables - relate indicators to latent constructs/factors - concerns about the underlying meaning and delineation of underlying psychological construct - like "factors" in factor analysis

Disturbance (D)

- leftover variance from a latent variable construct/factor

Error (E)

- leftover variance from a measurable variable

Questions that Structural Equation Model (SEM) can answer:

1) Does the model produce an estimated population covariance matrix that "fits" the sample data? 2) Which model best fits the data? 3) What is the percent of variance explained by the factors? 4) What is the reliability of the indicators?

What is Goodness-of-Fit statistics?

It is a statistical model describes how well it fits a set of observations.

Exogenous variable

Only serves as IVs in a structural model

How are SEM and FA similar?

These two analyses involve grouping variables to form latent constructs.

What are the potential problems when using a path analysis in analyzing a mediation effect?

1) Multicollinearity (high correlations among the IVs) 2) The Model omits variables that may impact two or more endogenous variables. 3) Interactions are rarely studied (??) 4) All variables are measured variables

Limitations of SEM

1) SEM is a confirmatory approach, hence cannot use to explore relationships among various variables. 2) Often strictly correlational 3) Generalizability to other population is poor 4) Sample size needs to be very large

Examples of Goodness-of-Fit Statistics

Chi-square Goodness-of-Fit Comparative Fit Index (CFI) Root Mean Square Error of Approximation

How to explore the Overall fit of a model?

Compare the correlations between each pair of variables (and for all variables) obtained by two different methods: 1) obtain bivariate correlation between each pair of variables ("obtained r") 2) get correlation between each pair of variables using the model ("implied r") When the obtained r and implied r are similar, then the model fits the data. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question.

Direct vs. indirect effects in a path analysis

Direct: IV1 -> DV Indirect: IV1 -> IV2 -> DV IV2 is a mediator

How can mediation and moderation be tested?

Hierarchical Regression, Structural Equation Model (SEM), Path Analysis

What is a comparative Fit Index (CFI)?

It is a Goodness-of-Fit statistical test that compares proposed model to an independence model (where nothing is related).

What is Root Mean Square Error of Approximation?

It is a Goodness-of-Fit statistical test that compares the estimated model to a saturated or perfect model.

What is a moderator?

It is referred to a 3rd variable, in which its value/level changes the nature of the relationship between an IV and a DV.

What is a mediator?

It is the 3rd variable that changes the significance of an IV's effect on the DV. ** Changes from significant to not-significant (complete mediation) ** Reduction in significance but still significant (partial mediation)

What is Overall Fit of the Model?

It is the extent that a model (SEM model or Path Analysis model in this case) fits the actual results in the researcher's data. In other words, the extent to which the model can plausibly explain the connections among the variables within a study.

What is mediation?

It is the process (or mechanism) in which a 3rd variable changes the significance of an IV's effect on the DV. ** Changes from significant to not significant (complete mediation) ** Reduction in significance but still significant (partial mediation).

What is moderation?

It is the process (or mechanism) in which the effect of an IV on a DV changes according to the value/level of a 3rd variable.

What does it mean when residuals covariance(s) in SEM is not symmetrically distributed?

It means that some covariance(s) are better estimated than others.

Endogenous variable

May serve as both IVs and DVs in a structural model

How are measured (observed) and latent variables depicted in a model diagram?

Measured variable are rectangular and latent variables are oval/circle.

How to measure Goodness-of-Fit?

Measuring the discrepancy between observed values and the values expected under the model in question.

What is the null and alternative hypotheses for a Chi-square Goodness-of-Fit statistics?

Null: The model fits the data in the population Alt: The model DOES NOT fit the data in the population (Hint: We want the model to fit the data, so not rejecting the null is our desired outcome.)

How to find out the magnitude of direct effect?

The beta weight of the independent variable of interest

What is the difference between Structural Equation Model (SEM) and path analysis?

The former includes both measured (observed) and latent variables. The latter includes only measured (observed) variables.

What are measured variables in SEM? What are measured variables in path analysis?

They are observed variables in SEM. They are predictors and outcomes in path analysis.

What are latent variables in SEM? What are latent variables in path analysis?

They are unobservable variables in SEM. They are factors or constructs in SEM. They drive the measured variables in measurement model of the SEM. There is no latent variables in path analysis!

How do we test a moderation?

To analyze the interaction effect of the IV and the presumed moderator variable, in relation to the DV.