Recent studies have emphasized that there is no justification for using the odds ratio (OR) as an approximation of the relative risk (RR) or prevalence ratio (PR). Erroneous interpretations of the OR as RR or PR must be avoided, as several studies have shown that the OR is not a good approximation for these measures when the outcome is common (> 10%). For multinomial outcomes it is usual to use the multinomial logistic regression. In this context, there are no studies showing the impact of the approximation of the OR in the estimates of RR or PR. This study aimed to present and discuss alternative methods to multinomial logistic regression based upon robust Poisson regression and the log-binomial model. The approaches were compared by simulating various possible scenarios. The results showed that the proposed models have more precise and accurate estimates for the RR or PR than the multinomial logistic regression, as in the case of the binary outcome. Thus also for multinomial outcomes the OR must not be used as an approximation of the RR or PR, since this may lead to incorrect conclusions.