Transcription of Linear Regression Analysis for Survey Data
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Linear Regression Analysis for Survey Data
Linear Regression Analysis for Survey DataProfessor Ron FrickerNaval postgraduate SchoolMonterey, California1 Goals for this Lecture Linear Regression How to think about it for Lickertscale dependent variables Coding nominal independent variables Linear Regression for complex surveys Weighting Regression in JMP2 Regression in Surveys Useful for modeling responses to Survey questions as function of (external) sample data and/or other Survey data Sometimes easier/more efficient then high-dimensional multi-way tables Useful for summarizing how changes in the Xs affect Y3(Simple) Linear Model General expression for a Linear model 0and 1are model parameters is the error or noise term Error terms often assumed independent observations from a distribution Thus And01iiiyx =++201~(,)iiYNx +2(0,)N ()01iiEYx =+4 Linear Model Can think of it as modeling the expected value of y,where on a 5-point Lickertscale, the ysare only measured very coarsely Given some data, we will estimate the parameters with coefficientswhere is the predicted value of y()01 |Eyxyx =+ y()01|Eyxx =+5 Estimating the Parameters Parameters are fit to minimize the sums of squared errors: Resulting OLSestimators:and111122111 1nnniiiiiiinniiiixyyxnxxn ===== = 01 yx = ()2011 niiiSSEyx = = + 6 Using LikertScale Survey Data as Dependent Variable in Regression Likertscale data is categorical (ordinal) If use as dependent
Naval Postgraduate School Monterey, California 1. Goals for this Lecture • Linear regression – How to think about it for Lickert scale dependent variables – Coding nominal independent variables • Linear regression for complex surveys • Weighting • Regression in JMP 2.
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