agridat (version 1.12)

foulley.calving: Calving difficulty by calf sex and age of dam

Description

Calving difficulty by calf sex and age of dam

Usage

data(foulley.calving)

Format

A data frame with 54 observations on the following 4 variables.

sex

calf gender

age

dam age factor, 9 levels

score

score for birthing difficulty, S1 < S2 < S3

count

count of births for each category

Details

These data are calving difficulty scores for purebred US Simmental cows.

The raw data show that the greatest calving difficulty is for male calves with young dams. Differences between male/female calving decreased with age of the dam.

The goodness of fit can be improved by using a scaling effect for age of dam.

Note: The paper by Foulley and Gianola has '21943' as the count for score 1, F, >8. This data uses '20943' so that the marginal totals from this data match the marginal totals given in the paper.

Examples

# NOT RUN {
data(foulley.calving)
dat <- foulley.calving

## Plot
d2 <- transform(dat, age=ordered(age, levels=c("0.0-2.0","2.0-2.5","2.5-3.0","3.0-3.5","3.5-4.0",
                                         "4.0-4.5","4.5-5.0","5.0-8.0","8.0+")),
                 score=ordered(score, levels=c('S1','S2','S3')))
require(reshape2)
d2 <- acast(dat, sex+age~score, value.var='count')
d2 <- prop.table(d2, margin=1)
require(lattice)
thm <- simpleTheme(col=c('skyblue','gray','pink'))
barchart(d2, par.settings=thm, main="foulley.calving",
         xlab="Frequency of calving difficulty", ylab="Calf gender and dam age",
         auto.key=list(columns=3, text=c("Easy","Assited","Difficult")))

## Ordinal multinomial model



## Note 1.0196-.3244 = 0.6952 matches Foulley's '2-3' threshold estimate

## Coefficients:
##                     Value Std. Error t value
## sexF            -0.500605    0.01518 -32.982
## age2.0-2.5      -0.234609    0.01350 -17.383
## age2.5-3.0      -0.758325    0.01803 -42.059
## age3.0-3.5      -1.037794    0.01649 -62.920
## age3.5-4.0      -1.218294    0.02218 -54.926
## age4.0-4.5      -1.271138    0.01960 -64.856
## age4.5-5.0      -1.374209    0.02589 -53.080
## age5.0-8.0      -1.416112    0.01529 -92.589
## age8.0+         -1.454782    0.02088 -69.680
## sexF:age2.0-2.5 -0.003035    0.01933  -0.157
## sexF:age2.5-3.0  0.076677    0.02611   2.937
## sexF:age3.0-3.5  0.080657    0.02464   3.274
## sexF:age3.5-4.0  0.135774    0.03293   4.124
## sexF:age4.0-4.5  0.124303    0.02982   4.169
## sexF:age4.5-5.0  0.198897    0.03831   5.192
## sexF:age5.0-8.0  0.135524    0.02280   5.943
## sexF:age8.0+     0.131033    0.03185   4.114

## Intercepts:
##       Value    Std. Error t value
## S1|S2   0.3244   0.0107    30.2148
## S2|S3   1.0196   0.0111    91.9371

## Residual Deviance: 216176.90
## AIC: 216214.90

if(require(ordinal)){
  m2 <- clm(score ~ sex*age, data=dat, weights=count, link='probit')
  summary(m2) # same as polr model
  predict(m2) # probability of each category
}

# }