This paper examines the various tests commonly used to select random parameters in choice modelling. The most common procedures for selecting random parameters are: the Lagrange Multiplier test as proposed by McFadden and Train (2000), the t-statistic of the deviation of the random parameter and the log-likelihood ratio test. The identification of random parameters in other words the recognition of preference heterogeneity among population is based on the fact that an individual makes a choice depending on her/his: tastes, perceptions and experiences. A simulation experiment was carried out based on a real choice experiment and the results indicated that the power of these three tests depends importantly on the spread and type of the tested parameter distribution.