# Multilevel analysis

#### noetsi

##### No cake for spunky
Comments on the p values for random effects say these are generally invalid with small sample sizes. We have about 70 units, our groups. Is that enough not to be small?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Would you be happy with a sample size of 70? What is the random effects variable(s)?

#### noetsi

##### No cake for spunky
It is 70 groups, there are thousands of cases (but groups is the key to the sampling as I understand it not cases). I have not decided yet what the predictors will be. We have actually 92 groups, but many of these are small.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
I think about it as a model in a model (between groups, within groups).

#### noetsi

##### No cake for spunky
It's strongly suggested that you not use the Wald p values for at least random effects in multilevel models (some suggest not using them for fixed effects either). Instead it is suggested you do a deviance (LR) test, testing one variable at a time (that is adding one to the model each time). II have found no guidance on what order makes the most sense. Two examples of this are below.

When you suspect a predictor has a fixed effect, and possibly a random one as well, do you have to first test the fixed effect with a LR then the random effect?

Do you have to test if there is a random intercept before you test if a slope is random? And if the intercept is not random, does it make sense to test for random slopes?

#### noetsi

##### No cake for spunky
one important element of ML models is seeing what percent of the group means fall where relative to the overall mean (or slope estimate). To make this calculation you use the standard deviation and the group mean (slope estimate). The software I use does not report a standard deviation it reports estimates and a standard error. How does the slope and its standard error relate to the standard deviation (this should be obvious, but its not to me).

This is what I am talking about....
"...as an example if the overall mean is .45 [this is one specific slope, this works for an intercept as well] and the standard deviation is .18 than 67 percent of the group means [the slope coefficients] are between .45-.18 and .45 + .18 and 95 percent lie between .45 –(2*.18) and .45 + (2*.18)."

#### hlsmith

##### Less is more. Stay pure. Stay poor.
You mean standard error here, right?

" standard deviation is .18 than 67 percent of the group means"

#### noetsi

##### No cake for spunky
The author used the term standard deviation (I just quoted them). I think this is the standard error reported with the slopes which I think is what hlsmith is suggesting.