Explained variance & VPC in ordered categorical response model
Posted: Mon Apr 24, 2017 1:39 pm
I want to examine
a) How much variance in my ordinal outcome variable is at individual level (level 1) vs. classroom level (level 2) vs school level (level 3)
b) How much variance at each of these levels is explained by adding certain predictors to my model.
With "normal" multilevel models I look at the variance components for this.
With the Ordered Categorical Response models (Ordered Multinomial in MLWin), I can't seem to find the individual level variance (thus both question A and question B cannot be answered).
In the LEMMA course section 9.3, MLwin practical, there is something about variance component models:
I see in text that: 3.29 is always assumed for a 3 level model (for me it would be a 4 level model with one additional "school" level), so that would answer question a (although I am not quite sure what this would look like in my 4-level).
I still don't understand how I can evaluate how much variance is explained at the individual level if more variables are added (if we assume this to be fixed).
Can anybody help me with this?
a) How much variance in my ordinal outcome variable is at individual level (level 1) vs. classroom level (level 2) vs school level (level 3)
b) How much variance at each of these levels is explained by adding certain predictors to my model.
With "normal" multilevel models I look at the variance components for this.
With the Ordered Categorical Response models (Ordered Multinomial in MLWin), I can't seem to find the individual level variance (thus both question A and question B cannot be answered).
In the LEMMA course section 9.3, MLwin practical, there is something about variance component models:
However, I can't figure out where the 3.29 is coming from.One way to assess the size of state effects is to compute the variance partition coefficient (VPC). The VPC is defined in C 9.3.1 and is interpreted as the proportion of the total (residual) variance in the underlying propensity to have high interest in EU elections that is attributable to differences between EU states. This underlying propensity is the latent continuous response variable that underlies the observed ordered variable (see C 9.1.5). The between-state variance is estimated as 0.229 which implies a VPC of 0.229/(0.229 + 3.29) = 0.065, so approximately 6.5% of the variation in EU election interest is due to between-state variation.
I see in text that: 3.29 is always assumed for a 3 level model (for me it would be a 4 level model with one additional "school" level), so that would answer question a (although I am not quite sure what this would look like in my 4-level).
I still don't understand how I can evaluate how much variance is explained at the individual level if more variables are added (if we assume this to be fixed).
Can anybody help me with this?