I intend to analyse the determinants of "children not attending school" after incorporating the effects of both children and household through binary logistic multilevel model.
1) Which kind of centring is necessary, group mean centring or grand mean centring? is it necessary in binary regressions to centre the data?
2) What will be the sequence for appropriate analysis? for example, I have found the ICC from the variance component model, which gives me clear sign to proceed towards regressing complex models like random intercept model or random intercept and slope model or random slope model. What should be the best sequence to estimate these models and why? is it necessary to follow a sequence? any relevant study which may include the justification or necessity of applying these models will be helpful. (I am lacking justification in the sequence of applying multilevel model, I have literature on the applied side and have done with it)
3) In simple logistic regression, we only discuss either a predictor is determinant of outcome variable or not. Here the analysis are made complex? correct me if I am wrong
1) Grand-mean,
2) Centering still applies in logistic,
3) Correct.
Hope this helps,
Matt
2. In multilevel modelling the sequence is very important. See McCoach (2010). The sequence you should follow is: null model, fixed slopes model, random slopes model, L2 predictors of the intercept, L2 predictors of the slopes.
The results of the null model support the decision to conduct multilevel analysis.
The results of the fixed slope model tell you which predictors you can specify as having random slopes.
Finally, because the intercept and the random slopes of the L1 model are used as criterions in the L2 equations, you should not make any modifications in L1 predictors or slopes when you are adding L2 predictors.
For example, if you remove one L1 predictor after you already introduced L2 predictors... you change the values that you attempted to predict at L2 (i.e., the intercepts and (possibly) the slopes of other L1 predictors).
McCoach, D. B. (2010). Hierarchical linear modeling. In G. R. Hancock & R. O. Mueller (Eds.) The reviewer’s guide to quantitative methods in the social sciences. (pp. 123-140). New York: Routledge.
I will have a go at question 1
Both are useful
a) grand mean centering is used to get an interpretable intercept when using continuous predictors, otherwise it (a value of zero) may be outside the range of the data; it can also help with more stable estimation, as you estimating a point that is 'inside' the data cloud of the Xs, not something that does not exist in the data
b) group mean centering is used to isolate the part of a level 1 variable that is really level 2 variation; ( and mutis mutandi lower and higher levels of variation in more complex models; ) lots of discussion in this paper ( and a lot of misunderstanding too)
Article Understanding and misunderstanding Group mean centering: a c...
You can use both together. That is create the group-mean variable for each level 2 entity based on a level 1 variable (x1subj),; subtract this from the level 1 variable to create the modified group centred level 1 variable (x1j - x1subj), then grand mean centre the level 2 variable ( x1subj - x1Grand mean). The include both x1j - x1subj and x1subj - x1Grand mean in the multilevel model, thereby getting an interpretable intercept, and the within and between estimate of a variable ostensibly measured at level 1.
Kelvyn Jones Thank-you for the answer, very informative and comprehensive.
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