Log-size of 79 Sitka spruce trees

The spruce data frame has 1027 rows and 6 columns. The data consists of measurements on 79 sitka spruce trees over two growing seasons. The trees were grown in four controlled environment chambers, of which the first two, containing 27 trees each, were treated with introduced ozone at 70 ppb whilst the remaining two, containing 12 and 13 trees, were controls.

spruce

Format

This data frame contains the following columns:

chamber

a numeric vector of chamber numbers

ozone

a factor with levels enriched and normal

id

a numeric vector of tree id

time

a numeric vector of the time when the measurements were taken, measured in days since Jan. 1, 1988

wave

a numeric vector of the measurement number

logsize

a numeric vector of the log-size

Source

Diggle, P.J., Liang, K.Y., and Zeger, S.L. (1994) Analysis of Longitudinal Data, Clarendon Press.

Examples

data(spruce)
spruce$contr <- ifelse(spruce$ozone=="enriched", 0, 1)
sitka88 <- spruce[spruce$wave <= 5,]
sitka89 <- spruce[spruce$wave > 5,]
fit.88 <- geese(logsize ~ as.factor(wave) + contr +
                          I(time/100*contr) - 1,
                id=id, data=sitka88, corstr="ar1")
summary(fit.88)
#> 
#> Call:
#> geese(formula = logsize ~ as.factor(wave) + contr + I(time/100 * 
#>     contr) - 1, id = id, data = sitka88, corstr = "ar1")
#> 
#> Mean Model:
#>  Mean Link:                 identity 
#>  Variance to Mean Relation: gaussian 
#> 
#>  Coefficients:
#>                     estimate  san.se      wald        p
#> as.factor(wave)1      4.0419 0.07909 2612.0473 0.000000
#> as.factor(wave)2      4.4653 0.07770 3302.9161 0.000000
#> as.factor(wave)3      4.8377 0.07729 3918.0609 0.000000
#> as.factor(wave)4      5.1744 0.08164 4017.0617 0.000000
#> as.factor(wave)5      5.3128 0.08286 4111.3549 0.000000
#> contr                -0.1931 0.23591    0.6701 0.413018
#> I(time/100 * contr)   0.2075 0.06922    8.9879 0.002718
#> 
#> Scale Model:
#>  Scale Link:                identity 
#> 
#>  Estimated Scale Parameters:
#>             estimate  san.se  wald         p
#> (Intercept)   0.3879 0.06428 36.42 1.587e-09
#> 
#> Correlation Model:
#>  Correlation Structure:     ar1 
#>  Correlation Link:          identity 
#> 
#>  Estimated Correlation Parameters:
#>       estimate   san.se  wald p
#> alpha   0.9749 0.005533 31048 0
#> 
#> Returned Error Value:    0 
#> Number of clusters:   79   Maximum cluster size: 5 
#> 

fit.89 <- geese(logsize ~ as.factor(wave) + contr - 1,
                id=id, data=sitka89, corstr="ar1")
summary(fit.89)
#> 
#> Call:
#> geese(formula = logsize ~ as.factor(wave) + contr - 1, id = id, 
#>     data = sitka89, corstr = "ar1")
#> 
#> Mean Model:
#>  Mean Link:                 identity 
#>  Variance to Mean Relation: gaussian 
#> 
#>  Coefficients:
#>                   estimate  san.se     wald       p
#> as.factor(wave)6    5.5066 0.09007 3737.366 0.00000
#> as.factor(wave)7    5.5189 0.08983 3774.170 0.00000
#> as.factor(wave)8    5.6826 0.08811 4159.433 0.00000
#> as.factor(wave)9    5.9040 0.08759 4543.137 0.00000
#> as.factor(wave)10   6.0433 0.08970 4538.681 0.00000
#> as.factor(wave)11   6.1299 0.08858 4789.231 0.00000
#> as.factor(wave)12   6.1311 0.08752 4907.011 0.00000
#> as.factor(wave)13   6.1336 0.08914 4734.329 0.00000
#> contr               0.3458 0.15009    5.309 0.02122
#> 
#> Scale Model:
#>  Scale Link:                identity 
#> 
#>  Estimated Scale Parameters:
#>             estimate  san.se  wald         p
#> (Intercept)   0.4024 0.06795 35.07 3.177e-09
#> 
#> Correlation Model:
#>  Correlation Structure:     ar1 
#>  Correlation Link:          identity 
#> 
#>  Estimated Correlation Parameters:
#>       estimate   san.se   wald p
#> alpha   0.9937 0.001998 247376 0
#> 
#> Returned Error Value:    0 
#> Number of clusters:   79   Maximum cluster size: 8 
#>