There is widespread consensus that using survey weights is necessary for descriptive inference (i.e., percentages, means) if the findings are to be generalized to the population from which the sample was drawn. There is less agreement on when and whether weights should be used with multivariate methods, such as linear or logistic regression analysis (Winship & Radbill, 1994; Gelman, 2007). If the sample selection and nonresponse are nonignorable, it is necessary to incorporate survey design features into the estimation of linear regression coefficients (Kott, 2007). Weighted regression, however, can produce inefficient standard errors of the estimates. Rather than use weighted regression, one alternative is to use a model-based approach that includes variables in a regression model that reflect sample design features (Gelman, 2007). In this paper, we use a series of simulation models based on the 2005 Current Population Survey to explore how sensitive a model-based strategy is to misspecification. A practical concern of a model-based strategy is that it requires an analyst to replicate many of the tasks of a survey statistician; when done incorrectly or with incomplete information, a model-based strategy could be risky. Our results show that, under some circumstances, the smaller standard errors from a model-based strategy may come at the cost of biased b-coefficients, so an unweighted approach should be used cautiously.