By Ulf Olsson
Generalized Linear versions (GLM) is a basic category of statistical types that incorporates many time-honored types as specified instances. for instance, the category of GLMs that incorporates linear regression, research of variance and research of covariance, is a unique case of GLIMs. GLIMs additionally comprise log-linear versions for research of contingency tables, prohib/logit regression, Poisson regression and lots more and plenty extra. This booklet provides an outline of GLMs and provides sensible examples in their use. even if the technique is utilized, the elemental idea of GLMs is gifted in a compact means. The exponential kin of distributions is mentioned in addition to the Maxium probability estimation and methods of assessing the healthy of the version. reaction variables as non-stop variables, as binary/binomial variables, as counts and as ordinal reaction variables are mentioned. there are lots of functional examples utilizing the Genmod software program of the SAS package deal. thought and functions of a extra advanced nature, like quasi-likelihood tactics, repeated measures types, combined types and research of survival info can be coated.
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Extra info for Generalized Linear Models: An Applied Approach
Example text
B The likelihood ratio test uses information on the log likelihood both at β and at 0. It compares the likelihoods L1 and L0 using the asymptotic χ2 distribution of −2 (log L0 − log L1 ). Thus, in a sense, the LR statistic uses more information than the Wald and score statistics. For this reason, Agresti (1996) suggests that the likelihood ratio statistic may be the most reliable of the three. c Studentlitteratur ° 49 2. 2: A likelihood function indicating information used in Wald, LR and score tests.
044. The difference between these p-values is explained by the fact that the Wald test essentially approximates the t distribution with a Normal distribution. The Poisson model gives a deviance of 14863 on 18 df. 0001. SHEEP Distribution POISSON Link Function LOG Dependent Variable COUNT Observations Used 20 Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF Deviance Scaled Deviance Pearson Chi-Square Scaled Pearson X2 Log Likelihood 18 18 18 18 . 5282 . 11. 1201 . 0001 . The scale parameter was held fixed.
Binomial : θ = log 1−p Normal : θ = µ so the canonical link is the identity link. The canonical links for a few distributions are listed in the table on page 41. Computer procedures such as Proc Genmod in SAS use the canonical link by default once the distribution has been specified. It should be noted, however, that there is no guarantee that the canonical links will always provide the “best” model for a given set of data. In any particular application the data may exhibit peculiar behavior, or there may be theoretical justification for choosing links other than the canonical links.