Hi there,
I was hoping someone on the forum might have some advice. I’m running a two-level multinomial model, and am trying to calculate predicted probabilities of each outcome for each of the higher-level units.
More specifically, my model has a nominal outcome - patient outcomes following surgery (different types of reoperation; no reoperation), with patients clustered within hospitals. I’ve been using ‘customised predictions’ to simulate predicted probabilities of the different outcomes from the model, and how these vary for different types of patients. I’m using the Lemma course Modules 7 and 10, and the MLwiN Manual Supplement as reference.
We’re also interested in exploring variation in predicted probabilities between hospitals – similar to the use higher-level residuals. I know the simulation method is for fixed-effects, but is there an approach I could use to also obtain predicted probabilities for each of my higher-level units (i.e. hospitals)? I do have the higher-level residuals, but the simulation method is conceptually very appealing, and would like to be consistent in my approach, where possible.
Many thanks,
Michael
Predicted probabilities for higher-level units in multinomial models
Re: Predicted probabilities for higher-level units in multinomial models
Several aspects to this
1) you can use coverage intervals in customised predictions to give between higher level unit overall differences on the probability scale but this will not give specific hospitals
2 You can use residuals at the higher level to get estimates of the specific hospital differences on the logit scale from the overall trend - exponentiate these to get odds and the overall odds will be 1 - these are very interpretable - so a value of 2 will be doubling the risk - I would recommenced this for what you are after
3 use ordinary predictions to get detailed effects (whatever you want fixed and/or random) on the logit scale and then use calc alogit to turn these to probabilities of the non referent category ; these will be the cluster specific predictions corresponding to the medians in the customised predictions facility not the means ( they will not be very different unless the higher level variance is large)
The customised prediction window was really designed to portray the relative size of the fixed effects. The simulations are needed there because of the need for population average values (means of the distribution taken account the higher level distributions) as well as cluster specific effects (the medians) which is what the model estimates.
See https://www.researchgate.net/publicatio ... N_Volume_2
for the PA and cluster specific distinction
Best
Kelvyn
1) you can use coverage intervals in customised predictions to give between higher level unit overall differences on the probability scale but this will not give specific hospitals
2 You can use residuals at the higher level to get estimates of the specific hospital differences on the logit scale from the overall trend - exponentiate these to get odds and the overall odds will be 1 - these are very interpretable - so a value of 2 will be doubling the risk - I would recommenced this for what you are after
3 use ordinary predictions to get detailed effects (whatever you want fixed and/or random) on the logit scale and then use calc alogit to turn these to probabilities of the non referent category ; these will be the cluster specific predictions corresponding to the medians in the customised predictions facility not the means ( they will not be very different unless the higher level variance is large)
The customised prediction window was really designed to portray the relative size of the fixed effects. The simulations are needed there because of the need for population average values (means of the distribution taken account the higher level distributions) as well as cluster specific effects (the medians) which is what the model estimates.
See https://www.researchgate.net/publicatio ... N_Volume_2
for the PA and cluster specific distinction
Best
Kelvyn