Question

What approaches are there by which coefficients are estimated for linear and logistic regression?

How is the deviance affected when an explanatory term is omitted (i know that it increases, but surely there is more to it?)

In what situations would we use Beta-binomial regression?

Answer 1

1.The logistic function also called the sigmoid function.In regression analysis logistic regression is estimating the parameters of a logistic model.

The approaches for linear regression are:

a.General linear regression or model,

b.Binomial regression,

c.Binary regression,

d.Simple regression,

e.Polynomial regression.

The approaches for logistic regression are:

a.Multinomial logistic,

b.Multinomial probistic,

c.Mixed logistic,

d.Mixed Probistic,

e.Ordered logistic,

f.Ordered Probistic.

2.A deviance for regression also impacts, based on the deviance or likelihood ratio chisquared statistic.

The deviance is given  as

di = s 2[yi log( yi µˆi ) + (ni − yi) log( ni − yi ni − µˆi )], with the same sign as the raw residual yi − yˆi . Squaring these

residuals and summing over all observations yields the deviance statistic. Observations with a deviance residual in excess of

two may indicate lack of fit.

3. The situations when beta binomial distribution  used in

a.Bayesian statistics,

b.Empirical Bayes methods and

c.Classical statistics to capture overdispersion in binomial type distributed data.