Sibling fixed effects

[Guest]

Ciao,

I have data on siblings who were raised in foster care which I intend to use to investigate mental health. In some cases the siblings are raised together in foster care. In other cases the siblings are raised separately. We have detailed information about the child through the age of 18 and the condition of the house they were brought up in. My inclination is to use a type of sibling fixed effects approach for siblings in the same foster care home to examine how the emphasis on chores, nutrition, spending, and others influence achievement orientation at the age of 18 but how do I address the siblings who are raised separately? This is what I have for siblings in the same household:

xtset sibsID
xtreg achievement chores nutrition spending, fe

sibsID is the same for siblings and each individual has their own personal ID (PID). Do I need to specify options for fe? I wonder if using fixed effects for the siblings in different homes will cancel out the effects I aim to estimate. Namely the condition of the household.


I hope to hear from you soon, Cheers

[Clyde Schechter]

Using fixed effects regression as you have shown will automatically adjust the analysis for any effects, observed or not, that are constant across all observations of the same sibling pair. For those who were raised together, this will include attributes of the household provided they lived in the same household for the entire period of observation. But as I understand it, you have longitudinal data on each person. So if a pair moved (together) from one household to another, then the household effects are no longer constant over the sibling pair's complete set of observations and therefore they are not fully adjusted for.

The truth is, what you have here is 3-level data. By using the -xt- commands you are mis-specifying the model so as to ignore the nesting of repeated measures within individuals and paying attention only to the nesting of individuals within pairs. If this were my data, I would probably used a 3-level random-effects model.

mixed achievement chores nutrition spending || sibsID: || individualID:

If, in addition, there is a variable in the data set that actually identifies the (potentially changing) household, I might go to a four-level model, with householdID nested in sibsID and individualID nested in householdID, and repeated observations on individuals as the lowest level. (Whether I would do this depends on how many sib pairs were raised together in multiple households.) Now, you might object that random effects models do not guarantee consistent estimation, except under assumptions not directly verifiable in the data. This is true, but the fixed-effects model you are estimating is known to be mis-specified, so it is unclear why consistent estimates of a wrong model are to be preferred to possibly inconsistent estimates of a model that has greater similarity to the data generating process. You can also mitigate this weakness of random effects models by adding more variables for the model to adjust for (assuming you have enough data to do that).

One other point, if you think that the effects of these variables might differ depending on whether the sibling pair was raised apart or separately, the most direct way to capture that in the model is to interact the predictor variables with an indicator for raised apart vs raised together.

[Guest]

Thank you Clyde for explicating. Now I should have been more specific and I apologize for not being so. The data are indeed longitudinal. However, I aim to begin the analysis by just looking at the household conditions of the foster home and the outcomes at the age of 18. We have repeated measures but I first want to look at this simple association.

Let's ignore that we have repeated measures just for now. Where we have two siblings raised together we can use the same home characteristics. For now let's assume the home characteristics don't change over time. And we want to examine mental health (a continuous measure that can be categorized) at age 18. In addition to this type of pairing, we have cases where two siblings were separated into two different foster homes. Now each sibling in this case would have different values for the home characteristics but they are still siblings. The ultimate objective is to cancel out the sibling effects and estimate only the effect of the home characteristics. This is where I thought fixed effects would come in. However using fixed effects when the siblings are in the same household opposed to when they are in different households was not trivial to me. Therefore in additional reading I wonder if I need to separate these cases and estimate the fixed effects models separately for siblings in the same houeshold and siblings in separate households?

Using fixed effects regression as you have shown will automatically adjust the analysis for any effects, observed or not, that are constant across all observations of the same sibling pair. For those who were raised together, this will include attributes of the household provided they lived in the same household for the entire period of observation. But as I understand it, you have longitudinal data on each person. So if a pair moved (together) from one household to another, then the household effects are no longer constant over the sibling pair's complete set of observations and therefore they are not fully adjusted for.

The truth is, what you have here is 3-level data. By using the -xt- commands you are mis-specifying the model so as to ignore the nesting of repeated measures within individuals and paying attention only to the nesting of individuals within pairs. If this were my data, I would probably used a 3-level random-effects model.

mixed achievement chores nutrition spending || sibsID: || individualID:

If, in addition, there is a variable in the data set that actually identifies the (potentially changing) household, I might go to a four-level model, with householdID nested in sibsID and individualID nested in householdID, and repeated observations on individuals as the lowest level. (Whether I would do this depends on how many sib pairs were raised together in multiple households.) Now, you might object that random effects models do not guarantee consistent estimation, except under assumptions not directly verifiable in the data. This is true, but the fixed-effects model you are estimating is known to be mis-specified, so it is unclear why consistent estimates of a wrong model are to be preferred to possibly inconsistent estimates of a model that has greater similarity to the data generating process. You can also mitigate this weakness of random effects models by adding more variables for the model to adjust for (assuming you have enough data to do that).

One other point, if you think that the effects of these variables might differ depending on whether the sibling pair was raised apart or separately, the most direct way to capture that in the model is to interact the predictor variables with an indicator for raised apart vs raised together.

[Clyde Schechter]

Well, if your goal is to estimate the housing effects, then including sibling pairs who were raised in the same household in a fixed-effects analysis (with sibling pair as the grouping variable defining the fixed effects), is pointless: as they do not vary on the predictor of interest, the predictor of interest is uninformative in the within-sibling pair analysis that a fixed-effects model provides. An analysis using only siblings raised separately, and including sibling-pair fixed effects and household variables as predictors will give you an estimate of the household variables' effects that is not confounded by any attributes of the sibling pair which they have in common.

As for the sibling pairs who were raised together, I don't see any role for analyzing them at all. They simply don't provide any information about the effects of the housing variables. If you include them in the analysis with the raised-apart pairs, they will not alter the results of the analysis. If you do a separate analysis on them the housing variables will be colinear with the fixed effects and will all be omitted from the analysis. Either way, you will learn nothing about housing effects from the pairs that were raised in the same house.