I used survey data for individuals to identify the significant variables that contribute to the evacuation decision. This was done through using backward step-wise method of the logistic regression. I am planning to use the model that was built on the significant variables to predict the evacuation participation rate using data at the aggregated level (neighborhood). Is there any way to preform such analysis? is there any article support this idea?
Thanks,
Khameis
Hi,
If individuals in the previously used data and the aggregate area overlap a lot, there might be a great consistency in significant variables, so you may just re-use the fitted model. Otherwise, there is no reason that the same model should apply. Another way to look at the problem is just re-run the backward selection procedure for the aggregated data and you will be able to check all this yourself.
Thanks for your reply. The issue is that I used (1,0) for the variable gender (male=1, female =0) in case of the individual data. In the aggregated data, I have the total for each gender type as (6,000 male), (4,000) female in the neighborhood, which is my aggregated level.
How can I apply the (1,0) to the aggregated data since I have it as a total?
I received a suggestion about multiplying the % of male for instance with the coefficient of the male within the logistic regression equation.
Y= = 1 /1+ Exp (1.240-0.13*(Elevation)-0.644*(Over 65)-0.719*0.60*(Male) +1.338*( Zone)).
I am not sure if this method is statistically right. I tested this method multiplying different % for male such as (0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,1) with the coefficient of gender while holding the rest of the variables constant to see how the predictions may change. I found that there is a slightly non-linear relationship in the predicted values using this method.
Is the slightly non-linear in the predicted values represent an issue?
Does multiplying the % of male to the coefficient of male in the logistic regression model breaks any statistical rule?
what gets modeled in logistic regression is the log of the odds ratio. this is linear in the covariates, including sex. so using .6 for male is ok in that sense. since you are really interested in the probability of evacuation, which is a nonlinear function of the log odds ratio, you could compute the probabilities separately for male and female, then take a weighted average.
as to the previous comment about using your original model on new people, what is the point of research if we can't use the results to give at least some idea of what would happen in a new situation? (though not to the 4th decimal place, of course).
more of an issue is the external validity of your study. how unique was the situation? new orleans is probably different from galveston, though one would expect some similarities, among which would be relationships with age, gender, and elevation. but history/experience is also important.
another issue that may be relevant here is 'once burned, twice shy,' meaning that even in the same city, one might expect the probability of evacuation to be higher if the last time was a disaster.
finally, your model does seem a bit strange, in that the intercept is positive, probably because most of the covariates are associated with not evacuating. also, is zone a binary variable? if not, you need to 'class' it or make indicators.
Thanks for your answer. I was using (1,0) for zone. Is there any article support using the % of male for example in the logistic regression equation for prediction?
i'm not sure about the literature, but as i said, it is completely legitimate to use .6 to estimate the log(odds) for the population, assuming that is the fraction male in the new population (i.e. the one for which you are trying to estimate the outcome using the survey data). ditto for all the other variables. they should be the values in the new population, not the sample you used for the survey.
again, if what you are really after is the probabilities of evacuation, i would suggest computing them using your coefficients for each subset of the population as defined by the summary data you have, then using a weighted average to get the predicted probability for the whole. from your coefficients, it looks as if elevation is a continuous measure, so you may need to group somehow. it is also possible that there is some interaction between elevation and age group. is elevation truly linear?
Khameis, you'd like to combine individual-level data with aggregate. Right? You might want to take a look at the hedonic pricing literature. Oftentimes, researchers are limited by data. So, they generally study parcel-level (individual houses) data alongside Census tract or school district-level data, where they regress individual housing prices on school district-level race indicators, for example. Hope that helps.
It would be appropriate to predict the aggregated outcome measure (i.e., evacuation participation rate at neighborhood level in your case) using the aggregated neighborhood level predictors. As discussed above, the percent of males and/or females is one of the examples of neighborhood level predictors. Similarly, you can aggregate other individual level predictors at neighborhood level and create the predictors at higher (neighborhood) level to predict evacuation rate. If you want to predict the individual level binary response variable (with 1 and 0 for evacuated or not evacuated) with the predictors at both levels (i.e., individual as well as neighborhood levels), you can use hierarchical logistic regression or hierarchical generalized linear model.
Best,
Bidya
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