1. The Trait Model of Change
David A. Kenny

2. Trait Model
All change is not real change, just random meaningless change (i.e., error).
There is an unchanging variable that causes the measurements at each time, i.e., a trait.
Time as a source of replication
Ordering of observations irrelevant
Some time points might be better indicators of the trait.

4. Identification Model identified with 3 or more waves.
Can allow for equal loadings (i.e., paths from the factor to the measures). With equal loadings only 2 waves needed.

5. Constraints
Besides setting loadings equal, error variances can be set equal.
Model with equal loadings and equal error variances called “compound symmetry” and is assumed in repeated measures analysis of variance.

6. Meaning of Error
Errors might be measurement errors or real variance that is totally unstable: a state.
The Trait Model is really a Trait-State Model

7. Multiple Indicator Trait(-State) Model
Three or more of the same indicators measured at two or more times.
Can have just two indicators per time, but loadings must be both fixed to one.
Errors of the same indicator allowed to be correlated across time.

9. Variance Decomposition
Total variance in a measure is a function of Trait, State, and Error.
True variance at each time is function of Trait and State:
Time 1: V(T) and V(S1)
Time 2: c2V(T) and V(S2)
Time 3: d2V(T) and V(S3)

10. Practicality
A trait model presumed in repeated measures analysis of variance
Hardly ever a reasonable model; so rarely a good fitting model
Other models, e.g., growth curve or autoregressive models, likely more realistic