Question
Ls4202_endsem_2017
please answer only question no.10. (5 marks)
7. The e plant species Spondias purpurea often suffers herbivore damage on both leaves and t borer Oncideres albomarginata. In a study of 220 individual plants, 25 of the 100 males showed significant damage due to herbivory while 40 females showed similar dauage Derive an appropriate regression model to test whether male and female plants suffered diferent levels of herbivory S. Write down the expression for the Akaike Information Criterion (AIC) and explain its componeats What is the fundamental basis of its use in model selection? Criterion (AIC) and explain its components 9. In the context of testing GLMs, what is residual deviance and null devianoe? How can you use this in hypothesis tests pertaining to the effect of a predictor variable X? 2 x 10. Overdispersion of data is á typical problem in Poisson Regression models. What does it mean, and how is it addressed it estimating the model'? K 11. Six morphometric measurements Y Ys.. , Y, were taken on a mature fower for n individuals of a plant species. Illustrate the principle and steps to compute Principal Components to order these n individuals in 2-dimensional space. 12. To test the null hypothesis of the equality of means, 14( 1.2, ., a) of a populations resulting from a treatments of a factor A, each with N(, 2), Analysis of Variance (ANOVA) is used, write down the ANOVA table for computing the different sources of variation in the data and explain the basis of statistical inference.
Explanation / Answer
overdispersion happens when there is greater variability in a data set than we expected it to have based on a given statistical model.
Overdispersion can be removed with an alternative model with additional free parameters. if you are using a Poisson regression model for count data then you can have a Poisson mixture model like negative binomial distribution in which the mean of the Poisson distribution can itself be thought of as a random variable drawn – in this case – from the gamma distribution thereby introducing an additional free parameter. This free parameter can solve your problem to a great extent.
There can be other methods also but all method generally revolve around the idea of introducing additional free parameters.
