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From: Bayesian Models for Astrophysical Data, Cambridge Univ. Press

(c) 2017,  Joseph M. Hilbe, Rafael S. de Souza and Emille E. O. Ishida

you are kindly asked to include the complete citation if you used this material in a publication

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Code 5.1 GLM logistic regression in R

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# Data
x <- c(13,10,15,9,18,22,29,13,17,11,27,21,16,14,18,8)
y <- c(1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0)

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# Fit
mu <- (y + 0.5)/2                                                      # initialize mu
eta <- log(mu/(- mu))                                            # initialize eta with the Bernoulli link

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for (i in 1:8) {
w <- mu*(- mu)                                                 # variance function
z <- eta + (y - mu)/(mu*(1-mu))                          # working response
mod <- lm(z ~ x, weights=w)                              # weighted regression
eta <- mod\$fit                                                      # linear predictor
mu <- 1/(1+exp(-eta))                                          # fitted value
cat(i, coef(mod), "\n")                                          # displayed iteration log

}

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# Output
summary(mod)

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Output on screen:

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Call:

lm(formula = z ~ x, weights = w)

Weighted Residuals:

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Min               1Q      Median              3Q           Max

-1.38600     -0.93301     0.08861      0.92411      1.25563

Coefficients:

Estimate         Std. Error    t value        Pr(>|t|)

(Intercept)        1.28606            1.65744      0.776          0.451

x                     -0.07915            0.09701     -0.816          0.428

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Residual standard error: 1.067 on 14 degrees of freedom Multiple R-squared: 0.0454, Adjusted R-squared: -0.02279 F-statistic: 0.6658 on 1 and 14 DF, p-value: 0.4282

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