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| [[attachment:hellevik.pdf | Hellevik (2009) ]] suggests that linear regression can be used with a binary outcome as opposed to logistic regression particularly for large samples. P-values between the two types of regression were found to be very close despite the ordinary least squares approach not incorporating heterogeneity of variance (where the variance of the proportions depends on the proportion) which is taken into account by logistic regression.[[attachment:mood.pdf | Mood (2010)]] also shows almost identical results using linear regression and logistic regression in Table 5 of the paper. | [[attachment:hellevik.pdf | Hellevik (2009) ]] suggests that linear regression can be used with a binary outcome as opposed to logistic regression particularly for large samples. P-values between the two types of regression were found to be very close despite the ordinary least squares approach not incorporating heterogeneity of variance (where the variance of the proportions depends on the proportion) which is taken into account by logistic regression.[[attachment:mood.pdf | Mood (2010)]] also shows almost identical results using linear regression and logistic regression in Table 5 of the paper and suggests linear regressions may be used on a binary outcome e.g. to make the result more interpretable. |
Linear regression as an alternative to logistic regression
Hellevik (2009) suggests that linear regression can be used with a binary outcome as opposed to logistic regression particularly for large samples. P-values between the two types of regression were found to be very close despite the ordinary least squares approach not incorporating heterogeneity of variance (where the variance of the proportions depends on the proportion) which is taken into account by logistic regression.Mood (2010) also shows almost identical results using linear regression and logistic regression in Table 5 of the paper and suggests linear regressions may be used on a binary outcome e.g. to make the result more interpretable.
On a related theme this research report by Jaeger suggests using mixed random effect models as opposed to the arcsine transformation when analyzing proportions in repeated measures ANOVAs.
Reference
Hellevik, O. (2009) Linear versus logistic regression when the dependent variable is a dichotomy. Qual Quant 43 59-74.
Mood, C. (2010) Logistic regression: why we cannot do what we think we can do, and what we can do about it. European Sociological Review 26(1) 67-82.