(Hari trying to make sense of Hari's queries)

> in the first (and second) page this is being described by saying that the Matrix for >the first model would be of a higher order (30 *6 vs 30*2) as compared >to second model.

I think am able to appreciate a little better as to why the Z matrix for first model is 30 *6. The error term for intercept and IQ is different for each CLASS (though within a class the error terms for 2 students are same) so the number of columns in Z = 2 * 3 (2 for Intercept and IQ while 3 for the 3 classes) for Model 1.

In second model the Z matrix dimension is 30*2, because not using any subject option means that variables defined on random statement dont vary from one CLASS to another. OTOH, there is a single variance for IQ and single variance for intercept which applies for all the 3 classes. So, number iof columns is equal to the number of variance terms which is 2

> I believe if somebody could tell me what the final combined equations for those 2 >models would be then I would be able to understand the "effect" of using subject option >in Random effect statement.

I can probably give it a shot (Can somebody verify my below guess is correct?) The model 2 equation would be Score_ij = ( b_00 + b_01 * IQ) + (e_0 + e_1 * IQ) + e_ij -- where i, j denote the ith student within the jth class)

>Judith's famous paper mentions the following "The SUB= option ..... ....... >Reading the above gave me a sense that if subject option is omitted in >a single Random statement of a model then it would be equivalent to >running a model with no Random statement. Am I correct?

Hari, I think you have NOT stated it in completely "correct" terms. I believe there are 3 ways one can write their model:- a) Include a random statement having lets say intercept and one IV along with a SUBJECT option b) Include a random statement having the same variables as in a) but with no subject option c) No random statement and the IV in random statement of a) is included in Model statement itself.

Each of the options a), b) and c) will yield different types of models. Specifically the fixed effects in all the three models will be same but the error components will be different. In a) 2 errors for each level of subject along with one residual/error for each individual, in b) 3 errors (inlcuding residual) for each individual while in c) a single residual/error component for each indivudal (plain OLS).

In short, omiiting subject option (case b) of above) is NOT equivalent to running a model with no random statement (case c) of above) - Am I correct?

Now the question comes as to why would somebody write a model with no subject option in random statement. Does this offer any advantages over a model with no random statement. How to INTERPRET a model of type b) in comparison to type c).

Can somebody please point out the glaring mistakes I may have made above.

Regards, Hari India