panel

Question 1

Cross sectional (about one occasion) fundamental problem

Answer 1

No within and between subject effects differences

Question 2

Panel data two main effect types

Answer 2

autoregressive, crossregressive

Question 3

the simplex model

Answer 3

assumes a steady rate of change with little external influences…

Question 4

The Quasi-Simplex Model

Answer 4

Extends the Simplex model by accounting for measurement error…

Question 5

Cross lagged panel model problems

Answer 5

1. problem = no difference between / within
2. does not take individual differences t = 1 into account

–> add random intercept

Question 6

trait state models key modelling ide

Answer 6

is that psychological constructs fluctuate along a stability continuum

Question 7

these models decompose the variance of constructs into

Answer 7

1. stable variance → the part of the variance due to the trait
2. non-stable variance → the part of the variance is due to the state and measurement error

Question 8

trait state model key aspects

Answer 8

1. usually involve higher-order and bi-factor structure
2. they require at least three measurement occasions
   → i.e., for some models even more, or additional constraints to aid convergence
3. the factor loadings of the stable trait latent variable are fixed to 1
   → i.e., indicating a constant effect of the construct across time
4. the factor loadings of the occasion specific measurement models are set equal over time
   → i.e., recall the weak invariance constraints applied for longitudinal measurements

Question 9

what type of invariance constraint applies for longitudinal measurement

Answer 9

weak invariance = loadings equal over time

Question 10

two types trait state model

Answer 10

1. The Stable Trait Autoregressive Trait and State (STARTS) (uni and multivariate)
2. The Trait-State Occasion (TSO) model

Question 11

Univariate starts: At each occasion, the measured variable is a function of three latent variables..

Answer 11

1. a time-invariant factor reflecting trait variance (i.e., 𝑆𝑇)
2. a time-varying factor reflecting an autoregressive effect (i.e., 𝐴𝑅𝑇)
3. an occasion-specific factor reflecting the state variance and measurement error (i.e., 𝑆)

Question 12

univariate starts how many measurement occasions

Answer 12

at least four, and equidistant

Question 13

difference multivariate and univariate starts model

Answer 13

based on measurement model, so accounting for measurement error -> so S, occasion specific variance is free of measurement error : i.e., it reflects occasion-specific fluctuations of the construct (with univariate it’s both fluctuations and measurement error)

Question 14

Identification recommendations…
in general

Answer 14

1. fix all factor loadings to 1
2. constrain the auto-regressive path coefficients of 𝐴𝑅𝑇 to equality across time (e.g., 𝑏)
   the equality constraint between auto-regressive paths ensures stationarity
   however, it may not be conceptually pertinent à it can be relaxed
   → two models (i.e., constrained and unconstrained) can be compared in terms of model fit
3. constrain variance of 𝐴𝑅𝑇 disturbances to equality across time (e.g., 𝑧)
4. constrain variance of 𝑆 to equality across time (e.g., 𝑎)

Question 15

difference trait-state occasion model and STARTS

Answer 15

in TSO the ART becomes ‘occasion’, and State disappears.

Question 16

Identification of the multivariate STARTS model
Requires several constraints to be imposed:

Answer 16

1. All STARTS’ factors are independent of one another (orthogonal).
2. The trait (TRAIT) factor loadings are all fixed to 1.
3. The autoregressive trait factor (ART) loadings are fixed at 1.
4. The STATE factor loadings are fixed at 1.
5. The autoregressive trait factor variances are constrained to equality in time.
6. The state factor variances are obliged to equality from one occasion through time.
7. The autoregressive coefficients are constrained to equivalence through time.
   PLUS: At least one weak invariance must be imposed (i.e., the loadings of item 2 in t1 = loadings of item 2 in t2 = loading of item 2 in t3 = loading of item 2 in t4 etc.).