1. ## Re: Multilevel analysis

This continues to confuse me. Some discussions of multilevel models make the distinction that random effects are important effectively when you don not have all the levels that exist [including ones that might exist in the future]. If you have all possible levels than you have a fixed effect and multilevel analysis is not important.

But other discussions of multilevel analysis focus on the impact of individual (level 1 variables) inside groups. So that if individual variables impact is influenced by groups then you have a random effect. Regardless of whether you have all the levels or not of a given variable. These seem incompatible usages. I often have population data. But it is likely the group, like area or unit, still influence individual variables. So should I use multilevel analysis or not in that case?

Maybe I am confusing multilevel analysis with the nature of random effects.

2. ## Re: Multilevel analysis

I thought the whole point of ML (multilevel analysis) is that the impact of the lower level variable on the DV varied at various levels of the upper level variable. But recent discussions I have seen say this is only true if there is an interaction effect between first and 2nd level and not otherwise.

Here is an example of what I mean.

This is what the author describes. "In a country where individuals rate their health more poorly on average, having less education has more negative effects relative to countries where individuals rate their health better on average...." that seems like an interaction to me. But the authors consider it a random effect a covariance.

https://www.childhealthdata.org/docs...f.pdf?sfvrsn=1

I did not see a slide number.

3. ## Re: Multilevel analysis

Maybe I should start with something simpler. What do random coefficients really tell you. That is the variances and covariance's that are random effects. You interpret a slope as they change in Y for a change in X. How do you practically not in theory, interpret the covariance's and variances that are random effects.

4. ## Re: Multilevel analysis

I may muddy this up since I haven't ran a MLM for quite awhile, but multiple logistic regression is fixed effects. Say you have another variable which is a level up (e.g., school, county, etc.) where the observations are nested in them and differ between the upper level variable groups. So now you calculate the effects within and between the group levels and you account for more variability. In addition, MLM allows you to control for random intercepts or not if necessary.

Sorry this is vague, but it is based on my recall.

5. ## Re: Multilevel analysis

You were my great hope in this hlsmith since spunky does not usually comment on ML threads
What you say is true I think. What confuses me is what exact the random terms are telling you, how you interpret their coefficients. It appears that to determine the effects of a first level on the DV inside a group variable you use interaction analysis rather than random effects. That said none of the sources I have found tell you how you do this. They say you specify an interaction term which tells you if this exist. But not how you know how the level two variables, or the groups which are not the same thing as the level 2 variables, actually influence the impact of the level 1 variables. Nothing like simple effects comes up.

I want to know how groups moderate level one predictors (how they influence their slopes) but nothing I have found so far deals with this. Random effects tell you to some extent how much they influence the level 1 predictors, but now, in what direction they do this.

The explanatory variable for differences in the intercept [level 2 predictors I think] need not be the same as those for the effectiveness of the treatment. For example, a good predictor of the intercept might be a girl’s height and a good predictor of the slope might be the type of treatment that a girl receives.
This is a problem I have with the combined equation. If the level 2 predictors indirectly influence the dependent variable through the level 1 predictors, but have no direct impact, they should not show up as significant in the combined equation. So they will be dropped despite being important. I do not see anything about estimating indirect effects in the ML literature.

6. ## Re: Multilevel analysis

This author has an interesting discussion of diagnostics in an exploratory model. But some of his comments are unclear to me. This discussion occurs in page 114 to 116 in the link below.

The author says
The vertical spread between the lines indicates between classroom variation in terms of intercepts and is consistent with a random intercept model
What does the vertical spread mean? The slope of the line, the difference between the high and low point of each line? I don't understand this.

Similarly on 115-116 the author says
The variability in the level of the classroom means differ between girls and boys; that is, the intercept variance may not be constant for gender. Most noticeable is the appearance of possibly two groups of boys—those with high segregation indices and those with lower values
I am not sure how he determines this. To me the difference is that at the top the slopes are downwards, but at the bottom they are largely upwards which suggest slope is the key. But I am not at all sure what the author is stressing here, it might also be a change in the vertical difference between the boy and girl side of the line.

http://courses.education.illinois.ed...M_GLMM_LMM.pdf

7. ## Re: Multilevel analysis

Noetsi,

Keep asking questions, I will do my best to mediocrically sp? answer them. Cross-level interaction terms are added by including a product term into the model statement with one of the terms being a fixed effect and the other listed in the random effects statement. I have only ran a few formal MLM models and most with binary outcomes, see the below link for a simple example looking at resident radiation exposure (continuous).

So exposures are nested in physicians and these physicians rotate through different services. So some services have higher risk for radiation exposure (e.g. vascular which uses fluoroscope) and some physicians due their behaviors/practices get exposed to more radiation (individual physicians are random effects). Now there is a multiplicative effect (interaction) for high risk residents are on high risk services. So exposures are synergic, more than just the two effects summed. I believe the interaction term is significant in the test statement, along with likely the -2LL, and you can probably kick out model probability predictions and also see this. I can't recall beyond predictions, if you can easily create a linear combination of terms from the combine model to get those outputted estimates easily.

http://www.jsurged.org/article/S1931...048-4/fulltext

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noetsi (06-07-2017)

9. ## Re: Multilevel analysis

I have decided to avoid binary ones, as the level of complexity in the discussions I have seen is much worse than linear dependent variables. I ran into a good book the other day on ML which is unfinished, if you are interested I can send it to you. The author raised questions that made me realize I have just touched the surface of ML models (and made me realize how little my class taught me).

This is the book I mentioned. I do not know if it was ever finished.
http://courses.education.illinois.ed...M_GLMM_LMM.pdf

10. ## Re: Multilevel analysis

I don't understand the logic here at all
On average no relationship between xi j and yi j may exist even though the effect of xi j randomly differs over clusters. In such a case, b for the xi j equals 0, but
the explanatory variable xi j should still be included in the model. For example, although gender is less important than ethnicity from a substantive point of view,
the exploratory analysis indicated that there might a random effect due to gender.
Why would you care if something that had no effect on Y, had a random effect.

11. ## Re: Multilevel analysis

Talking to spunky made me realize that this is what I really want to know. Our customers are nested inside units that provide services. I think, as do others, that units moderate service provision and other factors that influence customers. I need to model that. ML seemed ideal to do so, although the more I read about it the less I am sure of that.

I suspect that the groups generate different slopes for a given set of first level predictors. But we have too many groups to analyze each slope separately. I am looking for a simpler way to do that, ML was my approach because it seems to be used for that.

12. ## Re: Multilevel analysis

If you have a statistically significant random effect for a given variable, say age, does that mean its impact on the DV varies by some group variable? And do you know what group vary it varies by (I assume you have to have that group in the regression to test this, but nothing I have read addresses that point).

If you know that a predictor varies by a group is there any simple way to show the regressions between that predictor (controlling for other predictors) for each group level. I have tens of groups so a way to simplify this would be great.

13. ## Re: Multilevel analysis

I know little of moderator variables which seem like interaction to me but are different somehow. This which can be found at the top of p13 in the link below goes to the heart of my confusion on multilevel variables.

The first equation under 2.4 states that the relationship, as expressed by the slope coefficient between the popularity (Y) and the gnder (X) of the pupil, depends on the amount of experience of the teacher (Z). If is positive, the gender effect on popularity is larger with experienced teachers. Conversely if is negative, the gender effect on polarity is smaller with experienced teachers. Thus, the amount of experience of the teacher acts as a moderator variable for the relationship between popularity and gender....
http://joophox.net/mlbook2/Chapter2.pdf

What is the difference between a moderator effect and a cross level interaction? To me they seem the same. The impact of the predictor on Y at the first level will be influenced by the level of the 2nd level predictor in both moderation and cross level interaction. Just as importantly it would seem that a 2nd level variable might have limited direct effect on Y, but have significant impact on another predictor without being specified as an interaction effect. I am not sure how the combined equation handles this.

14. ## Re: Multilevel analysis

Effect modification (moderated relationship) is the same thing as interaction. Its more of a generic term in my opinion since you can have additive or multiplicative interactions and these can be antagonistic or synergistic.

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noetsi (06-09-2017)

16. ## Re: Multilevel analysis

So the way to test for moderation is to specify a cross sectional interaction? I keep thinking that random effects get at this which is very different.

17. ## Re: Multilevel analysis

You have to take my recommendations with a grain of salt, but you can have first level interactions or 2nd level interactions or cross level interactions. You just need to list them in the model.

I get why you are confused in regards to cross-level interactions, though this would consist of 1st and 2nd level variables interacting.