Dfbetas

Fit Analyses

Dfbetas

Dfbetas is a normalized measure of the effect of observations on the estimated regression coefficients. For linear models,

$B_{j , i} = \frac{b_{j}- b_{j(i)}}{s_{(i)} \sqrt{ ({X'}X)^{-1}_{jj}} }$

where (X'X)_jj^-1 is the jth diagonal element of (X'X)^-1. Values of B_{j , i} > 2 indicate observations that are influential in estimating a given parameter. A recommended size-adjusted cutoff is ${2 / \sqrt{n}}$ .

For generalized linear models,

$B_{j,i} = \frac{b_j- b_{j(i)}}{\sqrt{ \hat{\phi}_{(i)} (X'W{X})^{-1}_{jj}}}$

where W = W_o when the full Hessian is used and W = W_e when the Fisher's scoring method is used.

The dfbetas statistics are stored in variables named Byname_xname for each pair of response and explanatory variables, where yname is the response variable name and xname is the explanatory variable name. Up to the first two characters of the response variable name are used to create the new variable name.

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