Logit and probit models are most commonly used in ordinal regression, in most cases a model is fitted with both functions and the function with the better fit is chosen. However, probit assumes normal distribution of the probability of the categories of the dependent variable, when logit assumes the log distribution. Thus the difference between logit and probit is typically seen in small samples.
3. Negative log-log: This link function is recommended when the probability of the lower category is high. Mathematically the negative log-log is p(z) = –log (– log(z)).
4. Complementary log-log: This function is the inverse of the negative log-log function. This function is recommended when the probability of higher category is high. Mathematically complementary log-log is p(z) = log (– log (1 – z)).
5. Cauchit: This link function is used when the extreme values are present in the data. Mathematically Cauchit is p(z) = tan (p(z – 0.5)).
Logit and probit models are most commonly used in ordinal regression, in most cases a model is fitted with both functions and the function with the better fit is chosen. However, probit assumes normal distribution of the probability of the categories of the dependent variable, when logit assumes the log distribution. Thus the difference between logit and probit is typically seen in small samples.
3. Negative log-log: This link function is recommended when the probability of the lower category is high. Mathematically the negative log-log is p(z) = –log (– log(z)).
4. Complementary log-log: This function is the inverse of the negative log-log function. This function is recommended when the probability of higher category is high. Mathematically complementary log-log is p(z) = log (– log (1 – z)).
5. Cauchit: This link function is used when the extreme values are present in the data. Mathematically Cauchit is p(z) = tan (p(z – 0.5)).