In multivariate studies, like ordination or cluster analysis, the arcsine transformation is preferred.
Third, the logit scale correctly models the relationship between the mean and variance in binomial data, where variance is p(1-p)/n.
This is particularly useful in interpreting slopes from a logistic regression, in which the logit transformation is central. Second, the logit scale is more intuitive in that it is the log-odds.
This is particularly important where prediction is needed, as having a bounded scale could give nonsensical results (e.g., more than 100% or less than 0%). In constrast, the limits of the logit scale are negative infinity and positive infinity. For example, just as proportion is limited to 0–1, the arcsine square root scale is limited to 0 to pi. First, the logit scale covers all of the real numbers instead of being limited to a particular range. Recommendationsįor regression, the logit transformation is preferred for three reasons (Warton and Hui 2011). The curvature of the logit transformation is much more pronounced, so the logit transformation has a much stronger effect than the arcsine transformation. Points(p, pLogit.scaled, type='l', lwd=2, col='red')īoth transformations are essentially linear over the range of 0.3–0.7, with more curvature near the ends. Plot(p, pAsin.scaled, las=1, type='l', lwd=2, col='blue', xlab='p', ylab='p transformed') The base of the logarithm isn’t critical, and e is a common base. The logit transformation is the log of the odds ratio, that is, the log of the proportion divided by one minus the proportion. These transformations are also used for percentage data that may not follow a binomial distribution. Variance-stabilizing transformations are used to correct this problem in binomial data, and two of the most common variance-stabilizing transformations are the logit and arcsine transformations. Transformations of proportions and percentagesįor a binomial distribution, variance is a function of the mean, reaching a maximum value at a proportion of 0.5, and declining to zero at proportions of zero and one.
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