This paper examines various tests commonly used to select random parameters in choice modelling. The three 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 exercise was carried out based on a real case study  where cross-sectional and two different structures of panel data settings were used to examine the empirical size and power of the three tests.  The key results indicate that the power of these tests depends importantly on the spread and type of the parameter distribution.