If you have a binary DV the intercept is the negative of the threshold. You have an ordinal DV with 3 categories so two thresholds. You can computed the predicted probability for different random intercept values as shown on slide 66 of our Topic 7 handout, where slides 60-66 deal with understanding two-level logistic regression. See handout and video on our website.
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ljc posted on Monday, September 29, 2014 - 7:07 am
Slide 66 of topic 7 only has the patterns or cluster sizes. Am I looking in the wrong place?
Slide 66 refers to the Larsen-Merlo article - this is a good one to study. The slide looks like:
Understanding The Between-Level Intercept Variance • Intra-class correlation – ICC = 0.807/(π2/3+ 0.807) = 0.20 • Odds ratios – Larsen & Merlo (2005). Appropriate assessment of neighborhood effects on individual health: Integrating random and fixed effects in multilevel logistic regression. American Journal of Epidemiology, 161, 81-88. – Larsen proposes MOR: "Consider two persons with the same covariates, chosen randomly from two different clusters. The MOR is the median odds ratio between the person of higher propensity and the person of lower propensity." 66 MOR = exp( √(2* σ2) * Φ-1 (0.75) ) In the current example, ICC = 0.20, MOR = 2.36 • Probabilities – Compare β0j= -1 SD and β0j= +1 SD from the mean: For males at the aggression mean the probability varies from 0.14 to 0.50
ljc posted on Monday, September 29, 2014 - 11:38 am
Sorry, I hate to be dense, but I don't understand the &# notation.
I think your last sentence has the answer I am looking for which is, the formula for the predicted value for each cluster. I think I am supposed add (or subtract) the standard deviation to something, but I am not sure what.
Just as a note, I only have a random intercept in my particular example.
foe estimator being ML or MLR how to get: 1.) Predicted values (y-hat) and 2.) Residuals (resid)
e.g. I have a latent variable (LV) with three indicators. This LV is a dependent variable Y in the model. So to get the residual of this LV after being predicted by say another independent variable X which also latent with three indicator. i.e. Y by y1 y2 y3; X by x1 x2 x3; Y on X;
Just so, I found an interesting way to get this If X and Y were not latent variables. I can get this from the scatter plot-->save plot data.
However for latent variables this is not there! Please help. (in stata we get this using the predict command for non latent variable regressions)