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Produces 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

# S3 method for 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 glm
sieve(x,  ...)
# S3 method for 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

Heather Turner, Michael Friendly, with help from Achim Zeileis

See also

Examples

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)
#>           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
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)
#> Warning: no formula provided, assuming ~ses + mental

# or, show as a sieve diagram
mosaic(indep, labeling_args = long.labels, panel=sieve, gp=shading_Friendly)
#> Warning: no formula provided, assuming ~ses + mental


# 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")
#> Warning: no formula provided, assuming ~ses + mental


##  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")
 }
#> Initialising
#> Running start-up iterations..
#> Running main iterations........
#> Done
#> Warning: no formula provided, assuming ~ses + mental

 
 ############# UCB Admissions data, fit using glm()
 
 structable(Dept ~ Admit+Gender,UCBAdmissions)
#>                 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
 
berkeley <- as.data.frame(UCBAdmissions)
berk.glm1 <- glm(Freq ~ Dept * (Gender+Admit), data=berkeley, family="poisson")
summary(berk.glm1)
#> 
#> 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
#> 
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)
#> 
#> 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
#> 
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")
#> 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

# 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,]
#>      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
berk.glm3 <- glm(Freq ~ Dept * (Gender+Admit) + dept1AG, data=berkeley, family="poisson")
summary(berk.glm3)
#> 
#> 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
#> 
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")
#> 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