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2018 - American Sociological Association Annual Meeting Pages: unavailable || Words: 12241 words || 
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1. Wojtkiewicz, Roger. "Using Piecewise Linear Regression and Interrupted Regression to Understand Non-linearity" Paper presented at the annual meeting of the American Sociological Association Annual Meeting, Pennsylvania Convention Center & Philadelphia Marriott, Philadelphia, PA, Aug 09, 2018 Online <APPLICATION/PDF>. 2019-05-19 <http://citation.allacademic.com/meta/p1380173_index.html>
Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: The relationship between an interval independent variable and an interval dependent variable in linear regression appears to be straightforward at first glance. This paper explores the complexity in the effects of the interval independent variable that lies beneath this seemingly simple relationship. The paper considers two parallel approaches to relaxing linear constraints for the effect of an interval independent variable. The first is piecewise linear regression using knotted spline variables. The second is interrupted regression using a less common type of spline variable, the group spline. The paper shows that when all constraints are relaxed, a fully-specified piecewise linear regression model fits the data the same as a fully-specified interrupted regression model. The paper also shows that both fully-specified models stem from a fully-specified dummy variable model. Finally the paper shows that squared, cubed, and higher order polynomial variables also stem from the fully-specified dummy variable model. The fact that the polynomial variables are all constrained linear combinations of the same set of underlying variables explains the multicollinearity problem that arises when using polynomial variables.

2006 - The Midwest Political Science Association Pages: 26 pages || Words: 7091 words || 
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2. Liu, Baodong. "A Verification Study of Goodman Regression, Double-Regression and EI Extended Model" Paper presented at the annual meeting of the The Midwest Political Science Association, Palmer House Hilton, Chicago, Illinois, Apr 20, 2006 <Not Available>. 2019-05-19 <http://citation.allacademic.com/meta/p140700_index.html>
Publication Type: Conference Paper/Unpublished Manuscript
Abstract: This paper takes advantage of a unique opportunity to compare the controversial methods, including survey approach, by using aggregate as well as individual level data from an actual election. Our results show that EI basic model provided a better es

2012 - American Sociological Association Annual Meeting Pages: unavailable || Words: 11068 words || 
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3. Fossett, Mark., Fox, Amber. and Zhang, Wenquan (Charles). "Fractional Logit Regression and Logit Quantile Regression: New Options for Modeling Bounded Attainment Variables" Paper presented at the annual meeting of the American Sociological Association Annual Meeting, Colorado Convention Center and Hyatt Regency, Denver, CO, Aug 16, 2012 Online <APPLICATION/PDF>. 2019-05-19 <http://citation.allacademic.com/meta/p565833_index.html>
Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: Standard sociological research methods do not include many good options for dealing with bounded variables (e.g., proportions). Consequently, researchers often go forward with OLS regression, knowing it is inappropriate, but hoping for the best. Here we call attention to a new alternative –fractional logit regression. The technique draws on GLM methods to estimate non-linear, non-additive effects on the mean of a variable that is distributed continuously over a bounded range. It has several attractive qualities including: it always generates “in range” predictions, it does not require special treatment of boundary values, and it does not invoke strong assumptions about the distribution of the error term. Over the past decade the technique has been used with increasing regularity in economics. But it has yet to be applied in sociological research. In light of this, we review the technique of fractional logit regression and contrast it with several alternative techniques including OLS regression using the dependent variable (Y) in its original metric, OLS regression using logit-transformed values of Y, beta regression, and logit quantile regression. We note the strengths and weaknesses of the various alternatives and comment on issues researchers should consider when choosing a technique for analysis. We conclude that the technique of fractional logit regression has much to recommend it and that logit quantile regression can be a valuable supplement. We then present an empirical application to the analysis of White-Hispanic differences in the process of residential attainment by estimating effects of social characteristics on area proportion White.

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