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What is a Generalized Linear Model? A traditional linear model is of the form
where Yi is the response variable for the ith observation, xi is a column vector of explanatory variables for the ith response. Note that the p-dimensional vector xi is usually considered to be ?xed, or nonrandom. The p-dimensional vector β of unknown coe?cients is to be estimated on the basis of n observations. The errors i are assumed to be independent normally distributed zero-mean random variables with a constant variance. Hence, holds, that is, the expected value of the output random variable is a linear transformation of the input. All these assumptions are limitations and may not hold in some cases. In particular:
These limitations are dealt with in the setting of the generalized linear model (GLM) or their generalization, the generalized additive model (GAM). GLM have been introduced in Statistics by Nelder and Wedderburn (1972).
Likert scales is often used in the studies of attitudes in which the raw scores are based on the graded alternative responses to each of a series of queries. For instance, the sub
The Null Hypothesis - H0: γ 1 = γ 2 = ... = 0 i.e. there is no heteroscedasticity in the model The Alternative Hypothesis - H1: at least one of the γ i 's are not equal
The Null Hypothesis - H0: There is no autocorrelation The Alternative Hypothesis - H1: There is at least first order autocorrelation Rejection Criteria: Reject H0 if LBQ1 >
1) Question on the first day questionnaire asked students to rate their response to the question Are you deeply moved by the arts or music? Assume the population that is sampled
Case series : It is the series of reports on the condition of the individual patients made by treating physician. Such reports might be helpful and informative for the rare disease
Mauchly test is a test which a variance-covariance matrix of pair wise differences of responses in the set of longitudinal data is the scalar multiple of identity matrix, a proper
This is an approach to the modelling of time-frequency surfaces which consists of a Bayesian regularization scheme in which the prior distributions over the time-frequency coeffici
Bivariate survival data : The data in which the two related survival times are of interest. For instance, in familial studies of disease incidence, data might be available on the a
Lagrange Multiplier (LM) test The Null Hypothesis - H0: There is no heteroscedasticity i.e. β 1 = 0 The Alternative Hypothesis - H1: There is heteroscedasticity i.e. β 1
The number of passengers arriving at an airport terminal average 1200 each hour. To process passengers (check in, take luggage, etc) take an average of 6 minutes each. There are
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