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

If you work with some statistical software package, such SAS, STAT,  you could use 'least squares means'.  There are two mean functions for prediction based on the model your select. MEANS, all evaluation are based on your data used in the modeling, since you want to make the conclusion on the population rather than the data used in the analysis, you should not use 0.6 for the factor of (if male) , the Survey data usually have weight, the weighted average should be considered. Use aggregate weight percentage to replace 0.6 for the probability both male and female together.  There are also the question how to choose the value for Elevation, for the percentage of over65, etc.using sample mean or using  population mean. Or you just  fot the formula you give :Y= = 1 /1+ Exp (1.240-0.13*(Elevation)-0.644*(Over 65)-0.719*0.60*(Male) +1.338*( Zone))

The estimation is for both male and female, aged over 65( if choose 1),  with given (zone) value.

You can choose different value for predictors, for over65, would be 0-1, for male: 0-1,  but y and over65 is not linear. Using logistic regression, ln(p(x)/(1-p(x))=alpha+beta*x

The linear line is for ln(p(x)/(1-p(x)) with x, rather then P(x) with X. the larger slope at P=1/2, zero slope in both side near p(x)=0 or 1.

Another choice is the function of “Least Square Mean”.  Least squares means (LS Means) are actually a sort of SAS jargon. Least square means is actually referred to as marginal means (estimated marginal means). In an analysis of covariance model, they are the group means after having controlled for a covariate (i.e. holding it constant at some typical value of the covariate, such as its mean value).

Say we have three predict categorical factors; A (3 levels), B (2 levels)  and C (2 levels), one continuous factor z with mean =12.5. The least square means evaluate the means by choose 1/3 for all levels in A , ½ for all levels in B and C, the mean 12.5 for Z. They are adjustments. They could be marginal or combinations of the two or more factors, see following table, There is a option, you can choose different z values rather than mean.

                    u      A              B                                   A*b                       C            Z

                         1   2     3     1     2      (1,1),(1,2) (1,3) (2,1) (2,2) (2,3)  1  2

overall        1  1/3   1/3   1/3  1/2  1/2   1/6     1/6 1/6 1/6 1/6  1/6        1/2 1/2   12.5

B=1             1 1/3 1/3 1/3      1 0          1/3   1/3    1/3     0    0      0       1/2 1/2 12.5

B=2                1 1/3 1/3 1/3    1 0            0     0       0     1/3 1/3 1/3        1/2 1/2 12.5

A=1                1   0      0         1/2    1/2   1/2 1/2    0 0         0 0              1/2 1/2 12.5

.....

The calculation of LS mean is not easy to demonstrate. However, the LS mean should be used when the inferential comparison needs to be made. Typically, the means and LS means should point to the same direction (while with different values) for  comparison. Occasionally, they could point to the different directions (treatment A1 better than treatment A2  according to mean values; treatment A2 better than treatment A1 according to LS Mean).