Random effects assumption and its tests

[@Babette_Marty576]

Hi Mikko. Thank you so much for posting those videos. Knowledge is to valuable in this day and age and for you to post it for free is very generous! I myself have little statistics knowledge and was hoping you could help me with some questions that I have: I want to investigate whether changes in one variable between two time points (dependent) can be explained by changes in another variable between two time points (independent). I have repeated measures for each participant. Hausman Test with a p-Value of 0.8 indicates that a random effects model is the better choice. My questions are: 1. I have a lot of observed variables that highly correlated with my independent variable. Do I need to include those in the model? Am I otherwise in violation of the assumption that the unobserved heterogeneity is uncorrelated with my regressor? 2. How do I interpret the result correctly? If the intercept is 0.5 and the regression coefficient is 4. Is it like in linear regression: For every one unit increase in the independent variable, the dependent variable changes by the coefficient? How do I interpret the intercept? Thank you to much in advance!

[@mronkko]

You are welcome. 1) If your research design indicates that the variables should be included, then they need to be included. If they are highly correlated with the IV of interest, this becomes even more important. Otherwise you may be in violation of uncorrelated error term. 2) Yes, linear multilevel models are interpreted like regression. The intercept is typically not interpreted.

[@DM-qb6jm]

Thank you for these videos and resources! They are really helping me. In the second and third rows of Table 3 (likelihood ratio test and F test), am I correct in thinking we include the random effect u_j when fitting these models? After finding your videos, I looked up your paper, and I believe this is what your paper shows, but I wasn't sure if I was looking at the right part. (Thank you for providing sample code!!!) ### This is the code for the second row, likelihood ratio-test? m7

[@mronkko]

I think I did the video based on a version of the paper that was still under review. What you are referring to is Table 4 in the published paper. Anova does LR test for ML estimated models, so you are right. I do not think that we demonstrate F test in the example code, but Wald_test does Wald tests. If you want to learn more about F tests and see some example R code, see kzbin.info/www/bejne/fqO1eqh4Z9N2iqc If I remember correlty, the slides (linked in the video description) have some R code in the notes The answer to your conceptual question is yes. These tests test if all the contextual effects that you have in the model are zero.

[@DM-qb6jm]

​@@mronkko Thank you Dr. Rönkkö! I'm watching that linked video now and will check out the slides. I'm trying some of this out in R and had one other question. Am I correct in thinking that these procedures (of testing for all the contextual effects being 0) can't include any variable that is constant within the observations of each cluster/group (e.g., repeated measurements of people whose age and gender don't change during the study period)? I generated some sample data and had "age" as a covariate that was constant for each person's repeated measurement of the outcome y. After I created a new column with group mean of age, I realized it was identical to the existing "age" column (which seemed obvious in hindsight). Is our inability to include "age" in the test simply a limitation of this approach? Or, does it not really make sense, conceptually, to test for the contextual effect being 0 when the variable is constant across the group/cluster's repeated observations?

[@mronkko]

@@DM-qb6jmIf you have a variable that is constant within group, you can only estimate a between effect for that variable. But you cannot decompose it to within and contextual effects. As such, the existence of contextual effect cannot be tested at all. Note that the fact that a variable does not have within group variance does not mean that it does not have a within effect: it might, but the data does not allow us to say whether this is the case. (I am writing a paper that among other things talks abou this issue.)

[@DM-qb6jm]

@@mronkko thank you very much for the help with all my questions and for making these great resources!

[@AnnaKyiv]

thank you for this and other lectures. They help me much

[@mronkko]

You're very welcome!

[@chibuzochilaka3119]

Thank you so much for sharing this important idea. How can I communicate person information with you?

[@mronkko]

You are welcome. You can find my work email in the channel description.kzbin.infoabout

[@korenaklimczak]

I am a bit confused on why we can assume that between and within effects are equivalent when there are no contextual effects. What about phenomena like there being a negative between person-effect of higher typing speed being correlated with fewer mistakes, but positive within-effect of higher typing speed being correlated with greater mistakes? Or is that a different scenario with different principles being applied because it is correlation and not causation?

[@mronkko]

It is not an assumption but something that we know because the contextual effect is defined as an effect of a variable after controlling for its cluster mean. Your example has a big endogeneity problem because typing skills increase speed and decreases mistakes. But if we ignore that and just run regression, we would find a positive within effect and negative contextual effect.