Imagine that I have a regression model equation as,
Y= B0 + B1X1 + B2X2 + B3X3 + B4X4 + e
Where,
X1 is a variable with continuous value
X2 is a categorical variable at two levels such as gender
X3 is a variable with integer value
X4 is another categorical variable at two levels such as if a person is experienced or inexperience
I can solve it by using an OLS regression or using an unbalanced panel data. In the OLS regression, I can compare male group verses female group or experience group versus inexperience group which seems like I'm treating them as fixed effects in an unbalanced panel data. In that case, both of them are the same and I have to get the same results, am I right? Is there any advantages using OLS regression versus unbalanced panel data? Can I have a panel data without considering the time impact on the dependent variable? Thank you.
They are related in some ways;. I suggest you look at this link esp. at the bottom:
What is the difference between panel data analysis and regression analysis - Bing
Best, David Booth
Do you have the repeated measures that are characteristic of panel data? If so they are likely be dependent over time and that is why you need more than standard regression. If it is a cross section, you do not need panel-based procedures.
Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...
Article Fixed and Random effects models: making an informed choice
@ Professor Booth, Can you please let me have the link?
@ Professor Jones, The data is repeated measure but the dependent variable does not have any serial correlation over the time. Hence, I'm thinking to consider them as independent observations over the time. What are your thoughts?
Thank you.
Amir Abolhassani I am surprised that there are no enduring effects in you dependent variable, but you have not told us what it is nor how many individuals there are and how often have they been measured. How did you ascertain independence over time? You certainly cannot fit a full fixed effects to your data as you have time invariant Xs, viz gender. That is why I would use the REWB model to handle these situations flexibly.
Kelvyn Jones The sample size is 142 and there are 33 individuals over 5 years (each variable is measured once a year over the five years; however, there are some missing values for few observations for couple of years). Moreover, there are 11 independent variables which I just mentioned four of those. I evaluated 4-lag partial autocorrelation for the dependent variables for each individual over the study time and the lags were within 95% significance band indicating of no autoregressive. Are you still suggesting using REWB model? Please let me know if you need additional information. Thank you.
In theory: back to your original question. Fixed effects models (a dummy for each individual ) and standard multiple regression (no recognition whatsoever of repeated measures) can be seen as two ends of a continuum - no pooling and complete pooling; multilevel model - partial pooling - operates in the continuum between these extremes where the degree of pooling is influenced by the data as well as the specification of the model (https://www.reddit.com/r/statistics/comments/dntoxk/q_bayesian_hierarchical_models_no_pooling_vs/ )
So in my view, providing you can fit a RE model , you lose nothing by doing this and potentially have a lot to gain. This is especially the case for the time -invariant variables as the RE model recognizes the within-between nature of the data; e.g. you have at maximum 33 measures of gender. The standard multiple regression does not recognize this, while the full fixed effects model cannot estimate it due to exact collinearity. The RE model is also relatively forgiving about missingness as it is based on the MAR assumption.
In practice - it is very difficult to know what to recommend - you have ambitious plans for a complex model with 11 predictor variables, but very little data - especially for the time invariant variables - you have a maximum of 33 observations. I suspect, but do not know, that the autocorrelogram analysis silently used listwise deletion so that all records for an individual would be deleted if any measure was missing - this rapidly reduces power, and produces 'insignificant' results. It is is known that even small amounts of dependence have a large effect on standard errors. An ICC (the ratio of between variance to total (within + between) unexplained variance)of 10% is regarded as large.
So my advice - which may be of no practical use to you - is to collect more data and use the RE model.
Amir Abolhassani Could you send a link for the autocorrelation analysis - most software provides for a long time series on a single entity; it would be good to have a procedure that handles short series for multiple entities.
Kelvyn Jones Here is the autocorrelation analysis for a slightly larger population. It shows the autocorrelation based on ACF for different combination of categorical variables on dependent variable. As you can see, the lags are not calculated for the years that the data is not available for dependent variable (for instance page 1 lag 1 and page 7 lag 5 etc.). As I mentioned earlier, there is no autocorrelation over the years for different lags. Hence, I thought that we might be able to consider the problem as time-invariant and use a fixed effect (which the categorical variables are fixed effects) or a regression model. Please let me know if you need additional information. Thank you.
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