Psyo 373 final: structural equation modelling

What is a specific effect?

A specific effect is one that involves a relation between the systematic portion of a measurement error (i.e., uniqueness) and an observed or latent variable (draw diagram).

What are the differences between SEM and simple path analysis?

Path analysis does not include latent variables.

In the most general sense, what does SEM entail?

Path-analysis with latent variables.

What are correlated errors of measurement?

Correlated errors of measurement are exactly that. I will just draw a picture.

Why is SEM a better approach to assessing change than simple ANOVAs and t-tests?

1) We can factor out the error variance because we are looking at how latent variables change over time 2) We can determine if there is invariance. The change that is assessed might not just be change with regards to the level of the latent variable but the actual structure of the measurement model

What are the recommendations of the minimum amount of similarity that two measurement models should have to consider them as being invariant?

1) the same number of factors 2) the same pattern of factor loadings (i.e., which variables load on which factors) 3) at least one factor per loading that is equivalent across groups (e.g., factor loading for observed variable x is the same for group a and group b)

Why is the term "causal modeling" potentially misleading?

Because it implies that you can determine causation from that SEM, but this is not the case. The validity of causal claims rests on research design.

How is "isolation" at least partially achieved in SEM?

By including any possible confounding variables into the model. In your model you only draw an arrow between the variables that you think are causally responsible and not the other ones. If your model fits then this gives evidence that those other variables are not causally responsible. Remember correlation does not imply causation, but causation does imply correlation. If no correlation, then there can be no causation.

What are measurement models?

Hypotheses about the relations between a set of observed variables, such as ratings of questionnaire items, and the unobserved variables or constructs they were designed to measure. Draw one for bonus points.

In a full SEM, relationships between variables can be examined "at the latent level". Explain.

In SEM relations between latent variables can be analyzed. This is because SEM combines a measurement model with a structural model. When we look at variables at the latent level we are only looking at the common variance among variables. This removes all of the noise (unique variance) from the variable. Because error variance reduces the correlations that you will find between variables, SEM helps to maximize the coefficients that you find between variables.

How are correlated errors of measurement and specific effects discovered by researchers?

Many SEM packages/programs will notify the researcher of them

What is measurement invariance?

Measurement invariance concerns the degree to which a construct or a measure of a construct retains its meaning across groups or over time. It basically revolves around the question of whether the meaning of variable x is the same for groups a and b (a and b can also refer to the same group of people but tested at different times)

Why is measurement invariance important?

Measurement invariance is important because the comparison of means between groups or over time on a measure that is not invariant is meaningless. When there is a considerable departure from measurement invariance it is like comparing apples to oranges.

What are the advantages in using SEM to assess measurement stability?

One advantage is that SEM looks at the correlation between latent variables and therefore the measurement error associated with the observable variables has been removed. This will produce more accurate estimates of the correlation between variables because error leads to an underestimation of correlations. Another advantage is that SEM avoids the bias that comes from stability estimates that derive from the simple correlation between multiple assessments of a measure. For example, if errors between indicators of a measure are correlated (by some properties of them which lead to systematic bias), then test-retest (stability) correlation will be biased by the correlation between the errors of the indicators.

What is the structural model?

The structural model corresponds to aspects of a structural equation model that concern the relations among independent and dependent variables, either observed or latent. For example, the simple regression equation represents the simplest structural model, one in which an observed independent variable influences and observed dependent variable. However, structural models can be complex involving different types of relations between different types of variables (draw a little picture)

How are correlated errors of measurement and specific effects handled by researchers?

They will draw them into the model and rerun the model. However, it could be that there are some idiosyncrasies present in ones data that produces these correlations and thus replication is a must to determine whether there is a systematic phenomenon underlying the correlations or if it is just chance.

What general approach is used to assess measurement invariance?

To test whether two measures are invariant researchers first test whether the variance-covariance matrices for these two groups are the same. If this fails then there are a series of hypotheses that are tested to determine if there is measurement invariance.

What are latent variables?

Variables that are not observed directly but inferred from variables that are observed directly.