Contents
What is a covariance structure?
Covariance Structures are just patterns in covariance matrices. Some of these patterns occur often enough in some statistical procedures that they have names. For example, the Compound Symmetry structure just means that all the variances are equal to each other and all the covariances are equal to each other.
What is autoregressive covariance structure?
The autoregressive (Lag 1) structure considers correlations to be highest for time adjacent times, and a systematically decreasing correlation with increasing distance between time points. Between time 1 and time 3 the correlation would be less, and equal to ρ t 1 − t 3 .
What is covariance pattern model?
In covariance pattern models, the variance is not partitioned and the marginal covariance is directly modeled. The model is called a “covariance pattern model” because the researcher selects a covariance structure that patterns how the residuals are related to each other.
What is covariance structure analysis?
Covariance structure analysis is a statistical technique in which a theoretical model, or a covariance structure, is constructed, and the covariances predicted by the theoretical model are compared with those of the observed data.
Why are there no covariance terms between random effects?
Because the two random effects are separated into their own terms, no covariance term is included between them. In other words, only the diagonal of the variance-covariance matrix is estimated.
Which is the default structure for variance covariance?
The default variance-covariance structure is unstructured — that is, the only constraint on the variance-covariance matrix for an vector random effect with n levels is that is positive definite.
Are there any fixed effects that are allowed to vary randomly?
Here there are two fixed effects that are allowed to vary randomly, and one grouping factor g. Because the two random effects are separated into their own terms, no covariance term is included between them. In other words, only the diagonal of the variance-covariance matrix is estimated.
How are covariance terms specified in a formula?
Covariance terms are specified in the same formula as the fixed and random effects. Covariance terms are specified by the way the formula is written. Here there are two fixed effects that are allowed to vary randomly, and one grouping factor g.