Sampling - Sampling Issues In this module we discuss how to fix sampling issues The key methods you will learn are 1 Weighted least squares 2 Discrete

Sampling - Sampling Issues In this module we discuss how...

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Sampling Issues In this module, we discuss how to fix sampling issues. The key methods you will learn are: 1) Weighted least squares 2) Discrete Dependent variables (logit/probit models) 3) Selection models (Tobit models) Weighted Least Squares Suppose you were doing political polling where you knew that the true population split between the Democratic Party and Republican Party was 40% to 60%. And further suppose that when you did your polling, your sample was reversed, i.e., 60% democratic and 40% republican; and that each party received 70% of the vote for their own candidate. If you just report the sample mean (60%*70% + 40%*30%=54% for Democrat, 46% for Republican), you know that your estimate is biased. That is, if the true population weights were used, then the Republican would receive 54% and the Democrat would receive 46%. (BTW, this is one reason that polling is so hard, as the true percentages between the parties are not known, and many more demographic variables are needed to be considered, so the companies estimate them). The appropriate weight for each observation is then truevalue observed value = .4 .6 for the democratic voters. This is the general idea for weighted least squares (used by IRI, Neilson and others to adjust their panels for sampling issues). The likelihood function for regular regression is: 0.5 ∗( y ^ y ) 2 Whereas, for weighted least squares is: w ∗( y ^ y ) 2 with w be the weight for the observation. In SAS we use the WEIGHT clause in proc GLM to perform weighted least squares. Tobit Models One issue with weighted least squares is that you rarely know the true weights (especially if the weights are a function of many demographic variables). And, if you do not use the true weights, then the estimates are likely biased. While we will only focus on one form of the Tobit model (you will see others in different classes), the three types of Tobit models are: 1) Truncation models – this is where the observations are cut off at a certain level, e.g., you have a minimum purchase of $50 on your website, so you will not see any purchases less than $50. 2) Censoring models – this is related to what we call duration models and specifically credit cards, loyalty clubs, etc. In your data you may have left-censoring where you do not know when
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