Dear Egbe,

your question is far to broad to answer. I recommend to specify your question. What kind of survey? Single measurers or repeated measures? What kind of data? How many variables, etc.

Best,

Fabian

Dear Egbe

Firstly, your question is not clear. Based on my understanding of your question you need to apply Multinational logistic Regression, which can be discussed briefly as:

• Logistic regression is a form of multiple regression. It identifies the variables that collectively distinguish cases belonging to different categories of a nominal (or category) variable. For example, it could be used to identify the differentiating characteristics of psychology, sociology and physics students.
• Put another way, logistic regression identifies groups of variables that accurately classify people according to their membership of the different categories of a nominal variable.
• Multinomial logistic regression must be used when there are three or more categories for the dependent (predicted or criterion) variable.

Following

Egbe -

For establishment survey statistics considered for official statistics, there generally is one very good predictor/independent/regressor (x) variable that has a strong linear relationship (no intercept) with the variable of interest.  This can be true in a wider econometric setting.

 See chapter 7 of  Brewer, KRW (2002), Combined survey sampling inference: Weighing Basu's elephants, Arnold: London and Oxford University Press, and the first full paragraph of page 110 in particular. 

In the official statistics setting, often there are frequent samples and less frequent census collections of important variables, and the census variable can act as the regressor variable for the same item on the sample survey.  Sometimes an additional regressor helps, but perhaps not often.

Here is a presentation regarding examples of this: 

 https://www.researchgate.net/publication/319914742_Quasi-Cutoff_Sampling_and_the_Classical_Ratio_Estimator_-_Application_to_Establishment_Surveys_for_Official_Statistics_at_the_US_Energy_Information_Administration_-_Historical_Development

Cheers - Jim

For using auxiliary variables in a model-assisted design-based approach to survey data, see,  Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang, and Estimation in Surveys with Nonresponse, Carl-ErikSarndal and Sixten Lundstrom, John Wiley & Sons, 2005.  Others have written substantially on this as well. 

You might find the following entertaining and informative:

Ken Brewer's Waksberg Award article: 

 Brewer, K.R.W. (2014), “Three controversies in the history of survey sampling,” Survey Methodology,

(December 2013/January 2014), Vol 39, No 2, pp. 249-262. Statistics Canada, Catalogue No. 12-001-X.

http://www.statcan.gc.ca/pub/12-001-x/2013002/article/11883-eng.htm

(Note that the only purely model-based example in Ken Brewer's paper uses the classical ratio estimator, but he wrote much else about other models.) 

"Problems" might generally be finding good auxiliary data. But as noted earlier, for official statistics, that generally is not a problem.