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meglm postestimation - Stata

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16 <strong>meglm</strong> <strong>postestimation</strong> — Postestimation tools for <strong>meglm</strong><br />

Deviance residuals are calculated as<br />

ν D ij = sign(ν ij )√<br />

̂d<br />

2<br />

ij<br />

where the squared deviance residual ̂d 2 ij<br />

is defined as follows:<br />

family<br />

Squared deviance ̂d 2 ij<br />

bernoulli −2 log(1 − ̂µ ij ) if y ij = 0<br />

binomial<br />

gamma<br />

−2 log(̂µ ij ) if y ij = 1<br />

(<br />

rij<br />

2r ij log<br />

(<br />

yij<br />

2y ij log<br />

r ij − ̂µ ij<br />

)<br />

( )<br />

rij<br />

2r ij log<br />

̂µ ij<br />

if y ij = 0<br />

̂µ ij<br />

)<br />

+ 2(r ij − y ij ) log<br />

if y ij = r ij<br />

{ ( )<br />

yij<br />

−2 log − ̂ν }<br />

ij<br />

̂µ ij ̂µ ij<br />

( )<br />

rij − y ij<br />

r ij − ̂µ ij<br />

if 0 < y ij < r ij<br />

gaussian<br />

̂ν 2 ij<br />

nbinomial mean 2 log (1 + α̂µ ij ) α if y ij = 0<br />

( )<br />

( )<br />

yij<br />

1 +<br />

2y ij log −<br />

̂µ 2 ij<br />

α (1 + αy αyij<br />

ij) log<br />

1 + α̂µ ij<br />

otherwise<br />

nbinomial constant<br />

ordinal<br />

not defined<br />

not defined<br />

poisson 2̂µ ij if y ij = 0<br />

2y ij log<br />

(<br />

yij<br />

̂µ ij<br />

)<br />

− 2̂ν ij<br />

otherwise

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