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Data from infection from birth by Caesarian section, classified by Risk (two levels), whether Antibiotics were used (two levels) and whether the Caesarian section was Planned or not. The outcome is Infection (three levels).

Usage

data(Caesar)

Format

A 4-dimensional array resulting from cross-tabulating 4 variables for 251 observations. The variable names and their levels are:

NoNameLevels
1Infection"Type 1", "Type 2", "None"
2Risk"Yes", "No" (presence of risk factors)
3Antibiotics"Yes", "No" (were antibiotics given?)
4Planned"Yes", "No" (was the C section planned?)

Details

Infection is regarded as the response variable here. There are quite a few 0 cells here, particularly when Risk is absent and the Caesarian section was unplanned. Should these be treated as structural or sampling zeros?

Source

Fahrmeir, L. & Tutz, G. (1994). Multivariate Statistical Modelling Based on Generalized Linear Models New York: Springer Verlag, Table 1.1.

See also

caesar for the same data recorded as a frequency data frame with other variables.

Examples

data(Caesar)
#display table;  note that there are quite a few 0 cells
structable(Caesar)
#>                       Risk    Yes     No   
#>                       Planned Yes No Yes No
#> Infection Antibiotics                      
#> Type 1    Yes                   0  4   0  0
#>           No                   11 10   4  0
#> Type 2    Yes                   1  7   1  0
#>           No                   17 13   4  0
#> None      Yes                  17 87   1  0
#>           No                   30  3  32  9
require(MASS)
#> Loading required package: MASS

# baseline model, Infection as response
Caesar.mod0 <- loglm(~Infection + (Risk*Antibiotics*Planned), 
                     data=Caesar)

# NB: Pearson chisq cannot be computed due to the 0 cells
Caesar.mod0
#> Call:
#> loglm(formula = ~Infection + (Risk * Antibiotics * Planned), 
#>     data = Caesar)
#> 
#> Statistics:
#>                       X^2 df     P(> X^2)
#> Likelihood Ratio 85.10955 14 3.156586e-12
#> Pearson               NaN 14          NaN

mosaic(Caesar.mod0, main="Baseline model")


# Illustrate handling structural zeros
zeros <- 0+ (Caesar >0)
zeros[1,,1,1] <- 1
structable(zeros)
#>                       Risk    Yes     No   
#>                       Planned Yes No Yes No
#> Infection Antibiotics                      
#> Type 1    Yes                   1  1   1  0
#>           No                    1  1   1  0
#> Type 2    Yes                   1  1   1  0
#>           No                    1  1   1  0
#> None      Yes                   1  1   1  0
#>           No                    1  1   1  1

# fit model excluding possible structural zeros
Caesar.mod0s <- loglm(~Infection + (Risk*Antibiotics*Planned), 
                      data=Caesar, 
                      start=zeros)
Caesar.mod0s
#> Call:
#> loglm(formula = ~Infection + (Risk * Antibiotics * Planned), 
#>     data = Caesar, start = zeros)
#> 
#> Statistics:
#>                       X^2 df     P(> X^2)
#> Likelihood Ratio 78.89068  9 2.683409e-13
#> Pearson          77.55728  9 4.931611e-13

anova(Caesar.mod0, Caesar.mod0s, test="Chisq")
#> LR tests for hierarchical log-linear models
#> 
#> Model 1:
#>  ~Infection + (Risk * Antibiotics * Planned) 
#> Model 2:
#>  ~Infection + (Risk * Antibiotics * Planned) 
#> 
#>           Deviance df Delta(Dev) Delta(df) P(> Delta(Dev)
#> Model 1   85.10955 14                                    
#> Model 2   78.89068  9   6.218866         5         0.2855
#> Saturated  0.00000  0  78.890682         9         0.0000

mosaic (Caesar.mod0s)
#> Error in eval(expr, p): object 'zeros' not found

# what terms to add?
add1(Caesar.mod0, ~.^2, test="Chisq")
#> Single term additions
#> 
#> Model:
#> ~Infection + (Risk * Antibiotics * Planned)
#>                       Df     AIC    LRT  Pr(>Chi)    
#> <none>                   105.110                     
#> Infection:Risk         2 104.932  4.178    0.1238    
#> Infection:Antibiotics  2  72.187 36.922 9.603e-09 ***
#> Infection:Planned      2 107.742  1.368    0.5047    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# add Association of Infection:Antibiotics
Caesar.mod1 <- update(Caesar.mod0, ~ . + Infection:Antibiotics)
anova(Caesar.mod0, Caesar.mod1, test="Chisq")
#> LR tests for hierarchical log-linear models
#> 
#> Model 1:
#>  ~Infection + (Risk * Antibiotics * Planned) 
#> Model 2:
#>  ~Infection + Risk + Antibiotics + Planned + Risk:Antibiotics + Risk:Planned + Antibiotics:Planned + Infection:Antibiotics + Risk:Antibiotics:Planned 
#> 
#>           Deviance df Delta(Dev) Delta(df) P(> Delta(Dev)
#> Model 1   85.10955 14                                    
#> Model 2   48.18709 12   36.92246         2              0
#> Saturated  0.00000  0   48.18709        12              0

mosaic(Caesar.mod1, 
       gp=shading_Friendly, 
       main="Adding Infection:Antibiotics")