mosaic.glm: Mosaic plots for fitted generalized linear and generalized...
In vcdExtra: 'vcd' Extensions and Additions
Description
Usage
Arguments
Details
Value
Author(s)
See Also
Examples
Description
Procduces mosaic plots (and other plots in the strucplot framework)
for a log-linear model fitted with glm
or for a generalized nonlinear model fitted with gnm.
These methods extend the range of strucplot
visualizations well beyond the models that can
be fit with loglm.
They are intended for models for counts using the Poisson family (or quasi-poisson),
but should be sensible as long as (a) the response variable is non-negative and (b) the
predictors visualized in the strucplot are discrete factors.
Usage
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## S3 method for class 'glm'
mosaic(x, formula = NULL, panel = mosaic,
type = c("observed", "expected"),
residuals = NULL,
residuals_type = c("pearson", "deviance", "rstandard"),
gp = shading_hcl, gp_args = list(), ...)
## S3 method for class 'glm'
sieve(x, ...)
## S3 method for class 'glm'
assoc(x, ...)
Arguments
x
A glm or gnm object. The response variable, typically a
cell frequency, should be non-negative.
formula
A one-sided formula with the indexing factors of the plot
separated by '+', determining the order in which the variables are used in the mosaic.
A formula must be provided unless x$data
inherits from class "table" – in which case the indexing
factors of this table are used, or the factors in x$data
(or model.frame(x) if x$data is an environment) exactly
cross-classify the data – in which case this set of
cross-classifying factors are used.
panel
Panel function used to draw the plot for visualizing the observed values, residuals
and expected values. Currently, one of "mosaic", "assoc", or "sieve"
in vcd.
type
A character string indicating whether the
"observed" or the "expected" values of the table should be visualized
by the area of the tiles or bars.
residuals
An optional array or vector of residuals corresponding to the cells in the
data, for example, as calculated by residuals.glm(x), residuals.gnm(x).
residuals_type
If the residuals argument is NULL, residuals are calculated internally
and used in the display. In this case, residual_type can be "pearson",
"deviance" or "rstandard". Otherwise (when residuals is supplied),
residuals_type is used as a label for the legend in the
plot.
gp
Object of class "gpar", shading function or a corresponding generating function
(see strucplot Details and shadings).
Ignored if shade = FALSE.
gp_args
A list of arguments for the shading-generating function, if specified.
...
Other arguments passed to the panel function e.g., mosaic
Details
For both poisson family generalized linear models and loglinear models, standardized residuals
provided by rstandard
(sometimes called adjusted residuals) are often preferred because they have
constant unit asymptotic variance.
The sieve and assoc methods are simple convenience interfaces to this plot method, setting the panel argument accordingly.
Value
The structable visualized by strucplot is returned invisibly.
Author(s)
Heather Turner, Michael Friendly, with help from Achim Zeileis
See Also
glm, gnm, plot.loglm, mosaic
Examples
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GSStab <- xtabs(count ~ sex + party, data=GSS)
# using the data in table form
mod.glm1 <- glm(Freq ~ sex + party, family = poisson, data = GSStab)
res <- residuals(mod.glm1)
std <- rstandard(mod.glm1)
# For mosaic.default(), need to re-shape residuals to conform to data
stdtab <- array(std, dim=dim(GSStab), dimnames=dimnames(GSStab))
mosaic(GSStab, gp=shading_Friendly, residuals=stdtab, residuals_type="Std\nresiduals",
labeling = labeling_residuals)
# Using externally calculated residuals with the glm() object
mosaic.glm(mod.glm1, residuals=std, labeling = labeling_residuals, shade=TRUE)
# Using residuals_type
mosaic.glm(mod.glm1, residuals_type="rstandard", labeling = labeling_residuals, shade=TRUE)
## Ordinal factors and structured associations
data(Mental)
xtabs(Freq ~ mental+ses, data=Mental)
long.labels <- list(set_varnames = c(mental="Mental Health Status", ses="Parent SES"))
# fit independence model
# Residual deviance: 47.418 on 15 degrees of freedom
indep <- glm(Freq ~ mental+ses,
family = poisson, data = Mental)
long.labels <- list(set_varnames = c(mental="Mental Health Status",
ses="Parent SES"))
mosaic(indep,residuals_type="rstandard", labeling_args = long.labels, labeling=labeling_residuals)
# or, show as a sieve diagram
mosaic(indep, labeling_args = long.labels, panel=sieve, gp=shading_Friendly)
# fit linear x linear (uniform) association. Use integer scores for rows/cols
Cscore <- as.numeric(Mental$ses)
Rscore <- as.numeric(Mental$mental)
linlin <- glm(Freq ~ mental + ses + Rscore:Cscore,
family = poisson, data = Mental)
mosaic(linlin,residuals_type="rstandard",
labeling_args = long.labels, labeling=labeling_residuals, suppress=1, gp=shading_Friendly,
main="Lin x Lin model")
## Goodman Row-Column association model fits even better (deviance 3.57, df 8)
if (require(gnm)) {
Mental$mental <- C(Mental$mental, treatment)
Mental$ses <- C(Mental$ses, treatment)
RC1model <- gnm(Freq ~ ses + mental + Mult(ses, mental),
family = poisson, data = Mental)
mosaic(RC1model,residuals_type="rstandard",
labeling_args = long.labels, labeling=labeling_residuals, suppress=1, gp=shading_Friendly,
main="RC1 model")
}
############# UCB Admissions data, fit using glm()
structable(Dept ~ Admit+Gender,UCBAdmissions)
berkeley <- as.data.frame(UCBAdmissions)
berk.glm1 <- glm(Freq ~ Dept * (Gender+Admit), data=berkeley, family="poisson")
summary(berk.glm1)
mosaic(berk.glm1, gp=shading_Friendly, labeling=labeling_residuals, formula=~Admit+Dept+Gender)
# the same, displaying studentized residuals; note use of formula to reorder factors in the mosaic
mosaic(berk.glm1, residuals_type="rstandard", labeling=labeling_residuals, shade=TRUE,
formula=~Admit+Dept+Gender, main="Model: [DeptGender][DeptAdmit]")
## all two-way model
berk.glm2 <- glm(Freq ~ (Dept + Gender + Admit)^2, data=berkeley, family="poisson")
summary(berk.glm2)
mosaic.glm(berk.glm2, residuals_type="rstandard", labeling = labeling_residuals, shade=TRUE,
formula=~Admit+Dept+Gender, main="Model: [DeptGender][DeptAdmit][AdmitGender]")
anova(berk.glm1, berk.glm2, test="Chisq")
# Add 1 df term for association of [GenderAdmit] only in Dept A
berkeley <- within(berkeley, dept1AG <- (Dept=='A')*(Gender=='Female')*(Admit=='Admitted'))
berkeley[1:6,]
berk.glm3 <- glm(Freq ~ Dept * (Gender+Admit) + dept1AG, data=berkeley, family="poisson")
summary(berk.glm3)
mosaic.glm(berk.glm3, residuals_type="rstandard", labeling = labeling_residuals, shade=TRUE,
formula=~Admit+Dept+Gender, main="Model: [DeptGender][DeptAdmit] + DeptA*[GA]")
anova(berk.glm1, berk.glm3, test="Chisq")
Example output
Loading required package: vcd
Loading required package: MASS
Loading required package: grid
Loading required package: colorspace
Loading required package: gnm
ses
mental 1 2 3 4 5 6
Well 64 57 57 72 36 21
Mild 94 94 105 141 97 71
Moderate 58 54 65 77 54 54
Impaired 46 40 60 94 78 71
Warning message:
no formula provided, assuming ~ses + mental
Warning message:
no formula provided, assuming ~ses + mental
Warning message:
no formula provided, assuming ~ses + mental
Initialising
Running start-up iterations..
Running main iterations........
Done
Warning message:
no formula provided, assuming ~ses + mental
Dept A B C D E F
Admit Gender
Admitted Male 512 353 120 138 53 22
Female 89 17 202 131 94 24
Rejected Male 313 207 205 279 138 351
Female 19 8 391 244 299 317
Call:
glm(formula = Freq ~ Dept * (Gender + Admit), family = "poisson",
data = berkeley)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.4776 -0.4144 0.0098 0.3089 2.2321
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.27557 0.04248 147.744 < 2e-16 ***
DeptB -0.40575 0.06770 -5.993 2.06e-09 ***
DeptC -1.53939 0.08305 -18.536 < 2e-16 ***
DeptD -1.32234 0.08159 -16.207 < 2e-16 ***
DeptE -2.40277 0.11014 -21.816 < 2e-16 ***
DeptF -3.09624 0.15756 -19.652 < 2e-16 ***
GenderFemale -2.03325 0.10233 -19.870 < 2e-16 ***
AdmitRejected -0.59346 0.06838 -8.679 < 2e-16 ***
DeptB:GenderFemale -1.07581 0.22860 -4.706 2.52e-06 ***
DeptC:GenderFemale 2.63462 0.12343 21.345 < 2e-16 ***
DeptD:GenderFemale 1.92709 0.12464 15.461 < 2e-16 ***
DeptE:GenderFemale 2.75479 0.13510 20.391 < 2e-16 ***
DeptF:GenderFemale 1.94356 0.12683 15.325 < 2e-16 ***
DeptB:AdmitRejected 0.05059 0.10968 0.461 0.645
DeptC:AdmitRejected 1.20915 0.09726 12.432 < 2e-16 ***
DeptD:AdmitRejected 1.25833 0.10152 12.395 < 2e-16 ***
DeptE:AdmitRejected 1.68296 0.11733 14.343 < 2e-16 ***
DeptF:AdmitRejected 3.26911 0.16707 19.567 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 2650.095 on 23 degrees of freedom
Residual deviance: 21.736 on 6 degrees of freedom
AIC: 216.8
Number of Fisher Scoring iterations: 4
Call:
glm(formula = Freq ~ (Dept + Gender + Admit)^2, family = "poisson",
data = berkeley)
Deviance Residuals:
1 2 3 4 5 6 7 8
-0.75481 0.99471 1.96454 -3.15768 -0.03402 0.04449 0.15709 -0.22034
9 10 11 12 13 14 15 16
1.01273 -0.73839 -0.74367 0.54896 0.06760 -0.04741 -0.06911 0.05080
17 18 19 20 21 22 23 24
1.05578 -0.61236 -0.73617 0.42678 -0.20117 0.05113 0.19803 -0.05370
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.27150 0.04271 146.855 < 2e-16 ***
DeptB -0.40322 0.06784 -5.944 2.78e-09 ***
DeptC -1.57790 0.08949 -17.632 < 2e-16 ***
DeptD -1.35000 0.08526 -15.834 < 2e-16 ***
DeptE -2.44982 0.11755 -20.840 < 2e-16 ***
DeptF -3.13787 0.16174 -19.401 < 2e-16 ***
GenderFemale -1.99859 0.10593 -18.866 < 2e-16 ***
AdmitRejected -0.58205 0.06899 -8.436 < 2e-16 ***
DeptB:GenderFemale -1.07482 0.22861 -4.701 2.58e-06 ***
DeptC:GenderFemale 2.66513 0.12609 21.137 < 2e-16 ***
DeptD:GenderFemale 1.95832 0.12734 15.379 < 2e-16 ***
DeptE:GenderFemale 2.79519 0.13925 20.073 < 2e-16 ***
DeptF:GenderFemale 2.00232 0.13571 14.754 < 2e-16 ***
DeptB:AdmitRejected 0.04340 0.10984 0.395 0.693
DeptC:AdmitRejected 1.26260 0.10663 11.841 < 2e-16 ***
DeptD:AdmitRejected 1.29461 0.10582 12.234 < 2e-16 ***
DeptE:AdmitRejected 1.73931 0.12611 13.792 < 2e-16 ***
DeptF:AdmitRejected 3.30648 0.16998 19.452 < 2e-16 ***
GenderFemale:AdmitRejected -0.09987 0.08085 -1.235 0.217
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 2650.095 on 23 degrees of freedom
Residual deviance: 20.204 on 5 degrees of freedom
AIC: 217.26
Number of Fisher Scoring iterations: 4
Analysis of Deviance Table
Model 1: Freq ~ Dept * (Gender + Admit)
Model 2: Freq ~ (Dept + Gender + Admit)^2
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 6 21.735
2 5 20.204 1 1.5312 0.2159
Admit Gender Dept Freq dept1AG
1 Admitted Male A 512 0
2 Rejected Male A 313 0
3 Admitted Female A 89 1
4 Rejected Female A 19 0
5 Admitted Male B 353 0
6 Rejected Male B 207 0
Call:
glm(formula = Freq ~ Dept * (Gender + Admit) + dept1AG, family = "poisson",
data = berkeley)
Deviance Residuals:
1 2 3 4 5 6 7 8
0.00000 0.00000 0.00000 0.00000 -0.06316 0.08273 0.29514 -0.40088
9 10 11 12 13 14 15 16
0.55733 -0.41519 -0.41820 0.30511 -0.30655 0.21843 0.32036 -0.23141
17 18 19 20 21 22 23 24
0.69837 -0.41419 -0.49916 0.28628 -0.42032 0.10861 0.42684 -0.11382
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.23832 0.04419 141.157 < 2e-16 ***
DeptB -0.36850 0.06879 -5.357 8.47e-08 ***
DeptC -1.50215 0.08394 -17.895 < 2e-16 ***
DeptD -1.28509 0.08250 -15.577 < 2e-16 ***
DeptE -2.36552 0.11081 -21.347 < 2e-16 ***
DeptF -3.05899 0.15803 -19.357 < 2e-16 ***
GenderFemale -2.80176 0.23628 -11.858 < 2e-16 ***
AdmitRejected -0.49212 0.07175 -6.859 6.94e-12 ***
dept1AG 1.05208 0.26271 4.005 6.21e-05 ***
DeptB:GenderFemale -0.30730 0.31243 -0.984 0.325
DeptC:GenderFemale 3.40313 0.24615 13.825 < 2e-16 ***
DeptD:GenderFemale 2.69560 0.24676 10.924 < 2e-16 ***
DeptE:GenderFemale 3.52330 0.25220 13.970 < 2e-16 ***
DeptF:GenderFemale 2.71207 0.24787 10.941 < 2e-16 ***
DeptB:AdmitRejected -0.05074 0.11181 -0.454 0.650
DeptC:AdmitRejected 1.10781 0.09966 11.116 < 2e-16 ***
DeptD:AdmitRejected 1.15699 0.10381 11.145 < 2e-16 ***
DeptE:AdmitRejected 1.58162 0.11933 13.254 < 2e-16 ***
DeptF:AdmitRejected 3.16777 0.16848 18.803 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 2650.0952 on 23 degrees of freedom
Residual deviance: 2.6815 on 5 degrees of freedom
AIC: 199.74
Number of Fisher Scoring iterations: 3
Analysis of Deviance Table
Model 1: Freq ~ Dept * (Gender + Admit)
Model 2: Freq ~ Dept * (Gender + Admit) + dept1AG
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 6 21.7355
2 5 2.6815 1 19.054 1.271e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
vcdExtra documentation built on May 31, 2017, 4:57 a.m.
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Description Usage Arguments Details Value Author(s) See Also Examples
Description
Procduces mosaic plots (and other plots in the strucplot framework)
for a log-linear model fitted with glm
or for a generalized nonlinear model fitted with gnm.
These methods extend the range of strucplot
visualizations well beyond the models that can
be fit with loglm.
They are intended for models for counts using the Poisson family (or quasi-poisson),
but should be sensible as long as (a) the response variable is non-negative and (b) the
predictors visualized in the strucplot are discrete factors.
Usage
1 2 3 4 5 6 7 8 9 10 | ## S3 method for class 'glm'
mosaic(x, formula = NULL, panel = mosaic,
type = c("observed", "expected"),
residuals = NULL,
residuals_type = c("pearson", "deviance", "rstandard"),
gp = shading_hcl, gp_args = list(), ...)
## S3 method for class 'glm'
sieve(x, ...)
## S3 method for class 'glm'
assoc(x, ...)
|
Arguments
x |
A |
formula |
A one-sided formula with the indexing factors of the plot
separated by '+', determining the order in which the variables are used in the mosaic.
A formula must be provided unless |
panel |
Panel function used to draw the plot for visualizing the observed values, residuals
and expected values. Currently, one of |
type |
A character string indicating whether the
|
residuals |
An optional array or vector of residuals corresponding to the cells in the
data, for example, as calculated by |
residuals_type |
If the |
gp |
Object of class |
gp_args |
A list of arguments for the shading-generating function, if specified. |
... |
Other arguments passed to the |
Details
For both poisson family generalized linear models and loglinear models, standardized residuals
provided by rstandard
(sometimes called adjusted residuals) are often preferred because they have
constant unit asymptotic variance.
The sieve and assoc methods are simple convenience interfaces to this plot method, setting the panel argument accordingly.
Value
The structable visualized by strucplot is returned invisibly.
Author(s)
Heather Turner, Michael Friendly, with help from Achim Zeileis
See Also
glm, gnm, plot.loglm, mosaic
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 | GSStab <- xtabs(count ~ sex + party, data=GSS)
# using the data in table form
mod.glm1 <- glm(Freq ~ sex + party, family = poisson, data = GSStab)
res <- residuals(mod.glm1)
std <- rstandard(mod.glm1)
# For mosaic.default(), need to re-shape residuals to conform to data
stdtab <- array(std, dim=dim(GSStab), dimnames=dimnames(GSStab))
mosaic(GSStab, gp=shading_Friendly, residuals=stdtab, residuals_type="Std\nresiduals",
labeling = labeling_residuals)
# Using externally calculated residuals with the glm() object
mosaic.glm(mod.glm1, residuals=std, labeling = labeling_residuals, shade=TRUE)
# Using residuals_type
mosaic.glm(mod.glm1, residuals_type="rstandard", labeling = labeling_residuals, shade=TRUE)
## Ordinal factors and structured associations
data(Mental)
xtabs(Freq ~ mental+ses, data=Mental)
long.labels <- list(set_varnames = c(mental="Mental Health Status", ses="Parent SES"))
# fit independence model
# Residual deviance: 47.418 on 15 degrees of freedom
indep <- glm(Freq ~ mental+ses,
family = poisson, data = Mental)
long.labels <- list(set_varnames = c(mental="Mental Health Status",
ses="Parent SES"))
mosaic(indep,residuals_type="rstandard", labeling_args = long.labels, labeling=labeling_residuals)
# or, show as a sieve diagram
mosaic(indep, labeling_args = long.labels, panel=sieve, gp=shading_Friendly)
# fit linear x linear (uniform) association. Use integer scores for rows/cols
Cscore <- as.numeric(Mental$ses)
Rscore <- as.numeric(Mental$mental)
linlin <- glm(Freq ~ mental + ses + Rscore:Cscore,
family = poisson, data = Mental)
mosaic(linlin,residuals_type="rstandard",
labeling_args = long.labels, labeling=labeling_residuals, suppress=1, gp=shading_Friendly,
main="Lin x Lin model")
## Goodman Row-Column association model fits even better (deviance 3.57, df 8)
if (require(gnm)) {
Mental$mental <- C(Mental$mental, treatment)
Mental$ses <- C(Mental$ses, treatment)
RC1model <- gnm(Freq ~ ses + mental + Mult(ses, mental),
family = poisson, data = Mental)
mosaic(RC1model,residuals_type="rstandard",
labeling_args = long.labels, labeling=labeling_residuals, suppress=1, gp=shading_Friendly,
main="RC1 model")
}
############# UCB Admissions data, fit using glm()
structable(Dept ~ Admit+Gender,UCBAdmissions)
berkeley <- as.data.frame(UCBAdmissions)
berk.glm1 <- glm(Freq ~ Dept * (Gender+Admit), data=berkeley, family="poisson")
summary(berk.glm1)
mosaic(berk.glm1, gp=shading_Friendly, labeling=labeling_residuals, formula=~Admit+Dept+Gender)
# the same, displaying studentized residuals; note use of formula to reorder factors in the mosaic
mosaic(berk.glm1, residuals_type="rstandard", labeling=labeling_residuals, shade=TRUE,
formula=~Admit+Dept+Gender, main="Model: [DeptGender][DeptAdmit]")
## all two-way model
berk.glm2 <- glm(Freq ~ (Dept + Gender + Admit)^2, data=berkeley, family="poisson")
summary(berk.glm2)
mosaic.glm(berk.glm2, residuals_type="rstandard", labeling = labeling_residuals, shade=TRUE,
formula=~Admit+Dept+Gender, main="Model: [DeptGender][DeptAdmit][AdmitGender]")
anova(berk.glm1, berk.glm2, test="Chisq")
# Add 1 df term for association of [GenderAdmit] only in Dept A
berkeley <- within(berkeley, dept1AG <- (Dept=='A')*(Gender=='Female')*(Admit=='Admitted'))
berkeley[1:6,]
berk.glm3 <- glm(Freq ~ Dept * (Gender+Admit) + dept1AG, data=berkeley, family="poisson")
summary(berk.glm3)
mosaic.glm(berk.glm3, residuals_type="rstandard", labeling = labeling_residuals, shade=TRUE,
formula=~Admit+Dept+Gender, main="Model: [DeptGender][DeptAdmit] + DeptA*[GA]")
anova(berk.glm1, berk.glm3, test="Chisq")
|
Example output
Loading required package: vcd
Loading required package: MASS
Loading required package: grid
Loading required package: colorspace
Loading required package: gnm
ses
mental 1 2 3 4 5 6
Well 64 57 57 72 36 21
Mild 94 94 105 141 97 71
Moderate 58 54 65 77 54 54
Impaired 46 40 60 94 78 71
Warning message:
no formula provided, assuming ~ses + mental
Warning message:
no formula provided, assuming ~ses + mental
Warning message:
no formula provided, assuming ~ses + mental
Initialising
Running start-up iterations..
Running main iterations........
Done
Warning message:
no formula provided, assuming ~ses + mental
Dept A B C D E F
Admit Gender
Admitted Male 512 353 120 138 53 22
Female 89 17 202 131 94 24
Rejected Male 313 207 205 279 138 351
Female 19 8 391 244 299 317
Call:
glm(formula = Freq ~ Dept * (Gender + Admit), family = "poisson",
data = berkeley)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.4776 -0.4144 0.0098 0.3089 2.2321
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.27557 0.04248 147.744 < 2e-16 ***
DeptB -0.40575 0.06770 -5.993 2.06e-09 ***
DeptC -1.53939 0.08305 -18.536 < 2e-16 ***
DeptD -1.32234 0.08159 -16.207 < 2e-16 ***
DeptE -2.40277 0.11014 -21.816 < 2e-16 ***
DeptF -3.09624 0.15756 -19.652 < 2e-16 ***
GenderFemale -2.03325 0.10233 -19.870 < 2e-16 ***
AdmitRejected -0.59346 0.06838 -8.679 < 2e-16 ***
DeptB:GenderFemale -1.07581 0.22860 -4.706 2.52e-06 ***
DeptC:GenderFemale 2.63462 0.12343 21.345 < 2e-16 ***
DeptD:GenderFemale 1.92709 0.12464 15.461 < 2e-16 ***
DeptE:GenderFemale 2.75479 0.13510 20.391 < 2e-16 ***
DeptF:GenderFemale 1.94356 0.12683 15.325 < 2e-16 ***
DeptB:AdmitRejected 0.05059 0.10968 0.461 0.645
DeptC:AdmitRejected 1.20915 0.09726 12.432 < 2e-16 ***
DeptD:AdmitRejected 1.25833 0.10152 12.395 < 2e-16 ***
DeptE:AdmitRejected 1.68296 0.11733 14.343 < 2e-16 ***
DeptF:AdmitRejected 3.26911 0.16707 19.567 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 2650.095 on 23 degrees of freedom
Residual deviance: 21.736 on 6 degrees of freedom
AIC: 216.8
Number of Fisher Scoring iterations: 4
Call:
glm(formula = Freq ~ (Dept + Gender + Admit)^2, family = "poisson",
data = berkeley)
Deviance Residuals:
1 2 3 4 5 6 7 8
-0.75481 0.99471 1.96454 -3.15768 -0.03402 0.04449 0.15709 -0.22034
9 10 11 12 13 14 15 16
1.01273 -0.73839 -0.74367 0.54896 0.06760 -0.04741 -0.06911 0.05080
17 18 19 20 21 22 23 24
1.05578 -0.61236 -0.73617 0.42678 -0.20117 0.05113 0.19803 -0.05370
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.27150 0.04271 146.855 < 2e-16 ***
DeptB -0.40322 0.06784 -5.944 2.78e-09 ***
DeptC -1.57790 0.08949 -17.632 < 2e-16 ***
DeptD -1.35000 0.08526 -15.834 < 2e-16 ***
DeptE -2.44982 0.11755 -20.840 < 2e-16 ***
DeptF -3.13787 0.16174 -19.401 < 2e-16 ***
GenderFemale -1.99859 0.10593 -18.866 < 2e-16 ***
AdmitRejected -0.58205 0.06899 -8.436 < 2e-16 ***
DeptB:GenderFemale -1.07482 0.22861 -4.701 2.58e-06 ***
DeptC:GenderFemale 2.66513 0.12609 21.137 < 2e-16 ***
DeptD:GenderFemale 1.95832 0.12734 15.379 < 2e-16 ***
DeptE:GenderFemale 2.79519 0.13925 20.073 < 2e-16 ***
DeptF:GenderFemale 2.00232 0.13571 14.754 < 2e-16 ***
DeptB:AdmitRejected 0.04340 0.10984 0.395 0.693
DeptC:AdmitRejected 1.26260 0.10663 11.841 < 2e-16 ***
DeptD:AdmitRejected 1.29461 0.10582 12.234 < 2e-16 ***
DeptE:AdmitRejected 1.73931 0.12611 13.792 < 2e-16 ***
DeptF:AdmitRejected 3.30648 0.16998 19.452 < 2e-16 ***
GenderFemale:AdmitRejected -0.09987 0.08085 -1.235 0.217
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 2650.095 on 23 degrees of freedom
Residual deviance: 20.204 on 5 degrees of freedom
AIC: 217.26
Number of Fisher Scoring iterations: 4
Analysis of Deviance Table
Model 1: Freq ~ Dept * (Gender + Admit)
Model 2: Freq ~ (Dept + Gender + Admit)^2
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 6 21.735
2 5 20.204 1 1.5312 0.2159
Admit Gender Dept Freq dept1AG
1 Admitted Male A 512 0
2 Rejected Male A 313 0
3 Admitted Female A 89 1
4 Rejected Female A 19 0
5 Admitted Male B 353 0
6 Rejected Male B 207 0
Call:
glm(formula = Freq ~ Dept * (Gender + Admit) + dept1AG, family = "poisson",
data = berkeley)
Deviance Residuals:
1 2 3 4 5 6 7 8
0.00000 0.00000 0.00000 0.00000 -0.06316 0.08273 0.29514 -0.40088
9 10 11 12 13 14 15 16
0.55733 -0.41519 -0.41820 0.30511 -0.30655 0.21843 0.32036 -0.23141
17 18 19 20 21 22 23 24
0.69837 -0.41419 -0.49916 0.28628 -0.42032 0.10861 0.42684 -0.11382
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.23832 0.04419 141.157 < 2e-16 ***
DeptB -0.36850 0.06879 -5.357 8.47e-08 ***
DeptC -1.50215 0.08394 -17.895 < 2e-16 ***
DeptD -1.28509 0.08250 -15.577 < 2e-16 ***
DeptE -2.36552 0.11081 -21.347 < 2e-16 ***
DeptF -3.05899 0.15803 -19.357 < 2e-16 ***
GenderFemale -2.80176 0.23628 -11.858 < 2e-16 ***
AdmitRejected -0.49212 0.07175 -6.859 6.94e-12 ***
dept1AG 1.05208 0.26271 4.005 6.21e-05 ***
DeptB:GenderFemale -0.30730 0.31243 -0.984 0.325
DeptC:GenderFemale 3.40313 0.24615 13.825 < 2e-16 ***
DeptD:GenderFemale 2.69560 0.24676 10.924 < 2e-16 ***
DeptE:GenderFemale 3.52330 0.25220 13.970 < 2e-16 ***
DeptF:GenderFemale 2.71207 0.24787 10.941 < 2e-16 ***
DeptB:AdmitRejected -0.05074 0.11181 -0.454 0.650
DeptC:AdmitRejected 1.10781 0.09966 11.116 < 2e-16 ***
DeptD:AdmitRejected 1.15699 0.10381 11.145 < 2e-16 ***
DeptE:AdmitRejected 1.58162 0.11933 13.254 < 2e-16 ***
DeptF:AdmitRejected 3.16777 0.16848 18.803 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 2650.0952 on 23 degrees of freedom
Residual deviance: 2.6815 on 5 degrees of freedom
AIC: 199.74
Number of Fisher Scoring iterations: 3
Analysis of Deviance Table
Model 1: Freq ~ Dept * (Gender + Admit)
Model 2: Freq ~ Dept * (Gender + Admit) + dept1AG
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 6 21.7355
2 5 2.6815 1 19.054 1.271e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
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