mixed model with both fixed and random effect

[Lucia Lee]

Dear all,
As my dissertation is coming closer, here I am asking for your generous advice to go through this with STATA from this community.

I have two data sets, same data in different formats, from year 2000-2020 with 20+ donors and 100+ recipients.

1. Panel data (Donor - Recipient - Year - Amount that recipient A received from specific donor A, B, C...)

DonorA	Recipeint A	2000	USD 100M
DonorA	Recipient B	2000	USD 111M
DonorB	Recipient A	2000	USD 50M
DonorB	Recipient B	2000	USD 55M

STATA code I used: mixed ODAamount [independent variables] [control variables] i.year i.donor || recipient:, mle


2. Panel data (Recipient - Year - Total amount that recipient A received from all donors)

Recipient A	2000	USD 1000M
Recipien A	2001	USD 500M
Recipient B	2000	USD 55M

STATA code I used: mixed ODAamount [independent variables] [control variables] i.year || recipient1:, mle


So here's the real question.

What I am trying to anlayse in my paper is what recipients' characteristics affect the most on ODA allocation.
As I assume that there will be unobserved heterogeneity among recipients, so I put random effect for recipients and added year fixed effect.
But I am not sure if I should be adding fixed effect on donor (time invariant) or not when analysing explanatory variables regarding recipients' characteristics.
I would also like to ask if I can put 2 fixed effects (i.year and i.donor) with random effect as my code in 1.

I would really appreciate your comments on this.

Thank you.

[Erik Ruzek]

Including the indicators for donors makes sense to me because you want to eliminate any systematic differences in the outcome due to donors. Also the year indicators have the effect of eliminating outcome differences that are due to year-specific trends.

You mention that you are interested in understanding which recipient characteristics are associated with the outcome. How much variation in the outcome is at the recipient level (known as an intraclass correlation coefficient - ICC)? This tells you how much between-recipient variance you have to work with/to explain with your predictors. In this case, as a reader, I would want to know the ICC prior to accounting for year and donor effects and then after accounting for them.

mixed outcome || recipient1:, mle
estat icc   // "unconditional" ICC 
mixed outcome i.year i.donor || recipient1:, mle
estat icc   // "conditional" ICC after removing variance due to donor and year

The reason for comparing the two different ICCs is that knowing how much the year and donor effects reduce between-recipient variance in the outcome could be an important part of the story. If you have little between-recipient variance remaining after accounting for year and donor effects, then that tells you a lot about your outcome (it is temporally- and donor-dependent).

[Lucia Lee]

Dear Erik,

Thank you for the comment.

I followed your advice and

First Model without Donor and Year Effects
ICC Value: 0.0342847

Second Model with Donor and Year Fixed Effects
Variance at the Recipient Level (var(_cons)): 0.3318987
Residual Variance (var(Residual)): 5.164403
After calcuation: about 6.04% of the total variance in the logged total ODA commitment per capita can be attributed to differences between the recipients when accounting for donor and year effects.

I am not sure if I should change everything at this point as it seems low.

[Erik Ruzek]

In my research areas of education and psychology, this is a fairly typical ICC value. I would proceed with analyzing the data with the year and donor indicators. Just keep in mind that 94% of the variance in your outcome is within recipients, and accordingly, you have much more variance to explain at that level than at the between-recipient level. You would need to add time-varying predictors to get at the within-recipient variance as recipient characteristics, if time-invariant, only explain the variance at the between-recipient level.