Description Usage Arguments Value Note See Also Examples
Diagnostics for binomial regression
Returns diagnostic measures for a binary regression model by covariate pattern
1 2 3 4 
x 
A regression model with class 
... 
Additional arguments
which can be passed to:

byCov 
Return values by covariate pattern, rather than by individual observation. 
A data.table
, with rows sorted by dBhat.
If byCov==TRUE
, there is one row per covariate pattern
with at least one observation.
The initial columns give the predictor variables 1 ... p.
Subsequent columns are labelled as follows:
y 
The actual number of observations with y=1 in the model data. 
P 
Probability of this covariate pattern.

n 
Number of observations with these covariates.

yhat 
The predicted number of observations having
a response of y=1, according to the model.
yhat[i] = n[i] * P[i] 
h 
Leverage, the diagonal of the hat matrix used to generate the model: H = V^0.5 X (X'VX)^1 X'V^0.5 Here ^1 is the inverse and
' is the transpose of a matrix.
v[i][i] = n[i]P[i] * (1  P[i]) Leverage H is also the estimated covariance matrix of
Bhat.
h[i] = x[i]  mean(x), 0.1 < P[i] < 0.9 That is, leverage is approximately equal to the distance of
the covariate pattern i from the mean mean(x).

Pr 
The Pearson residual, a measure of influence. This is: Pr[i] = (y[i]  ybar) / SD[y] where ybar and SD[y] refer
to the mean and standard deviation of a binomial distribution.
E(y=1) = ybar = yhat = nP and SE[y] = (nP(1P))^0.5 Thus: Pr[i] = (y[i]  n[i]P[i]) / (n[i]P[i](1  P[i])^0.5) 
dr 
The deviance residual, a measure of influence: dr[i] = sign(y[i]  yhat[i]) * d[i]^0.5 d[i] is the contribution of observation i
to the model deviance.
In logistic regression this is: y[i] = 1 > dr[i] = (2 * log (1 + e^f(x)  f(x)))^0.5 y[i] = 0 > dr[i] = (2 * log (1 + e^f(x))) where f(x) is the linear function of the predictors 1 ... p: f(x) = B[0] + B[1][i] * x[1][i] + ... + B[p][i] * x[p][i] this is also: dr[i] = sign(y[i]  yhat[i]) [2 * (y[i] * log(y[i] / n[i] * p[i])) + (n[i]  y[i]) * log((n[i]  y[i]) / (n[i] * (1  p[i])))]^0.5 To avoid the problem of division by zero: y[i] = 0 > dr[i] = (2 * n[i] *  log(1  P[i]) )^0.5 Similarly to avoid log(Inf): y[i] = n[i] > dr[i] = (2 * n[i] *  log(P[i]) )^0.5 The above equations are used when calculating dr[i] by covariate group. 
sPr 
The standardized Pearson residual.
sPr[i] = Pr[i] / (1  h[i])^0.5 
sdr 
The standardized deviance residual.
sdr[i] = dr[i] / (1  h[i])^0.5 
dChisq 
The change in the Pearson chisquare statistic with observation i removed. Given by: dChi^2 = sPr[i]^2 = Pr[i]^2 / (1  h[i]) where sPr[i] is the standardized Pearson residual,
Pr[i] is the Pearson residual and
h[i] is the leverage.

dDev 
The change in the deviance statistic
D = SUM dr[i]
with observation i excluded.
dDev[i] = sdr[i]^2 = dr[i]^2 / (1  h[i]) 
dBhat 
The change in Bhat
with observation i excluded.
dBhat = h[i] * sPr[i]^2 / (1  h[i]) where sPR[i] is the standardized Pearson residual.

By default, values for the statistics are calculated by
covariate pattern.
Different values may be obtained if
calculated for each individual
obervation (e.g. rows in a data.frame
).
Generally, the values calculated by
covariate pattern are preferred,
particularly where the number of observations in a group is >5.
In this case Pearsons chisquared and the deviance statistic
should follow a chisquared distribution with i  p degrees of freedom.
1 2 3 4 5 6 7 8 9 10 11 12  ## H&L 2nd ed. Table 5.8. Page 182.
## Pattern nos. 31, 477, 468
data(uis)
uis < within(uis, {
NDRGFP1 < 10 / (NDRGTX + 1)
NDRGFP2 < NDRGFP1 * log((NDRGTX + 1) / 10)
})
(d1 < dx(g1 < glm(DFREE ~ AGE + NDRGFP1 + NDRGFP2 + IVHX +
RACE + TREAT + SITE +
AGE:NDRGFP1 + RACE:SITE,
family=binomial, data=uis)))
d1[519:521, ]

(Intercept) AGE NDRGFP1 NDRGFP2 IVHXprevious IVHXrecent RACEother
1: 1 27 0.7142857 0.24033731 0 1 0
2: 1 26 0.3125000 0.36348463 0 1 0
3: 1 33 5.0000000 8.04718956 0 0 0
4: 1 28 0.9090909 0.08664562 0 1 0
5: 1 33 0.3225806 0.36496842 0 1 0

517: 1 46 0.6250000 0.29375227 0 1 1
518: 1 40 10.0000000 23.02585093 1 0 0
519: 1 40 10.0000000 23.02585093 0 1 1
520: 1 41 10.0000000 23.02585093 0 1 1
521: 1 24 0.4761905 0.35330350 1 0 0
TREATlong SITEB AGE:NDRGFP1 RACEother:SITEB y P n yhat
1: 0 0 19.28571 0 0 0.03236867 1 0.03236867
2: 1 0 8.12500 0 0 0.02857757 1 0.02857757
3: 0 1 165.00000 0 1 0.46433729 2 0.92867458
4: 0 0 25.45455 0 0 0.04242218 1 0.04242218
5: 0 0 10.64516 0 0 0.04048063 1 0.04048063

517: 1 1 28.75000 1 1 0.22337160 1 0.22337160
518: 1 1 400.00000 0 1 0.22004414 1 0.22004414
519: 0 0 400.00000 0 1 0.16759820 1 0.16759820
520: 0 0 410.00000 0 1 0.16262781 1 0.16262781
521: 0 1 11.42857 0 1 0.03262591 1 0.03262591
Pr dr h sPr sdr dChisq
1: 0.1828974 0.2565312 0.004923582 0.1833493 0.2571650 0.03361696
2: 0.1715176 0.2408064 0.006861302 0.1721090 0.2416368 0.02962152
3: 0.1011269 0.1009980 0.019260759 0.1021151 0.1019849 0.01042750
4: 0.2104793 0.2944428 0.004987819 0.2110062 0.2951799 0.04452363
5: 0.2053983 0.2874814 0.005968712 0.2060140 0.2883432 0.04244177

517: 1.8646300 1.7314263 0.053366647 1.9164688 1.7795620 3.67285273
518: 1.8826956 1.7400731 0.052449879 1.9341004 1.7875837 3.74074442
519: 2.2285985 1.8900719 0.043542719 2.2787624 1.9326158 5.19275812
520: 2.2691430 1.9059334 0.047027078 2.3244574 1.9523939 5.40310206
521: 5.4452261 2.6163519 0.009167194 5.4703578 2.6284273 29.92481422
dDev dBhat
1: 0.06613386 0.0001663348
2: 0.05838834 0.0002046463
3: 0.01040093 0.0002047859
4: 0.08713117 0.0002231890
5: 0.08314180 0.0002548438

517: 3.16684074 0.2070578164
518: 3.19545552 0.2070619666
519: 3.73500393 0.2364003227
520: 3.81184196 0.2666309753
521: 6.90862989 0.2768646411
(Intercept) AGE NDRGFP1 NDRGFP2 IVHXprevious IVHXrecent RACEother
1: 1 40 10.0000000 23.0258509 0 1 1
2: 1 41 10.0000000 23.0258509 0 1 1
3: 1 24 0.4761905 0.3533035 1 0 0
TREATlong SITEB AGE:NDRGFP1 RACEother:SITEB y P n yhat
1: 0 0 400.00000 0 1 0.16759820 1 0.16759820
2: 0 0 410.00000 0 1 0.16262781 1 0.16262781
3: 0 1 11.42857 0 1 0.03262591 1 0.03262591
Pr dr h sPr sdr dChisq dDev dBhat
1: 2.228599 1.890072 0.043542719 2.278762 1.932616 5.192758 3.735004 0.2364003
2: 2.269143 1.905933 0.047027078 2.324457 1.952394 5.403102 3.811842 0.2666310
3: 5.445226 2.616352 0.009167194 5.470358 2.628427 29.924814 6.908630 0.2768646
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.