When your question is to fit a model to predict count variable, with few assumptions, poisson regression is a solution.
One of the strong assumptions in possion regression is that the mean and variance of dependent variable are equal. If observed variance is greater than mean, then it is an indication of overdispersion and variance being less than mean indicates underdispersion. When such situations arise, use of negative binomial regression is suggested.
Ratio of deviance to its degrees of freedom is a statistic used to understand overdisperion. If this ratio is equal to 1, then there is no overdispersion. If the ratio is greater than 1, then there is overdispersion and if ratio is less than 1 then it is an indication of underdispersion.
We use natual log as link function in Poisson regression. So estimated parameters are on log scale and hence before interpretation, we need to transform. Poisson regression uses maximum likelihood estimation method to estimate parameters.
Poisson regression is also suitable to model rate data. e.g Traffic Police department may capture data of number of accidents occured, then rate would be number of accidents per hour. Rate is counts per unit time. This time variable is called as offset variable.
Negative Binomial Regression, Zero inflated regression model, OLS regression are some other techniques used to model count data.
One of the strong assumptions in possion regression is that the mean and variance of dependent variable are equal. If observed variance is greater than mean, then it is an indication of overdispersion and variance being less than mean indicates underdispersion. When such situations arise, use of negative binomial regression is suggested.
Ratio of deviance to its degrees of freedom is a statistic used to understand overdisperion. If this ratio is equal to 1, then there is no overdispersion. If the ratio is greater than 1, then there is overdispersion and if ratio is less than 1 then it is an indication of underdispersion.
We use natual log as link function in Poisson regression. So estimated parameters are on log scale and hence before interpretation, we need to transform. Poisson regression uses maximum likelihood estimation method to estimate parameters.
Poisson regression is also suitable to model rate data. e.g Traffic Police department may capture data of number of accidents occured, then rate would be number of accidents per hour. Rate is counts per unit time. This time variable is called as offset variable.
Negative Binomial Regression, Zero inflated regression model, OLS regression are some other techniques used to model count data.
