# [R] lme problem

Henric Nilsson henric.nilsson at statisticon.se
Wed Apr 13 18:16:52 CEST 2005

```Milos Zarkovic said the following on 2005-04-12 16:40:

> I have recently started using R. For the start I have tried to
> repeat examples from Milliken &  Johnson "Analysis of
> Messy Data - Analysis of Covariance", but I can not replicate
> it in R. The example is chocolate chip experiment. Response
> variable vas time to dissolve chocolate chip in seconds (time),
> covariate was time to dissolve butterscotch chip (bstime), and
> type was a type of chocolate chip. Problem is that I obtain
> different degrees of freedom compared to one in the book.
> Could it be sum of squares problem (type III vs. type I)?
> Milliken & Johnson use SAS for calculations and this
> is program the used:
>
> proc mixed data=mmacov method=type3; class type;
> model time=type bstime*type/solution noint.

The PROC MIXED code above doesn't correspond to the R code below.

> My R code is:
>
> LME.1=lme(time~bstime:type+type-1,data=CCE,random=~1|type)

In your `lme' call, a random effect for each of the levels of `type' has

Since the analysis performed by PROC MIXED doesn't have any random
effects it can be reproduced in R using the `lm' function. The results
below match those of Milliken & Johnson p. 49 (using PROC MIXED) and the
results on p. 43 (using PROC GLM).

> fit <- lm(time ~ bstime:type + type - 1, data = CCE)
> summary(fit)

Call:
lm(formula = time ~ bstime:type + type - 1, data = CCE)

Residuals:
Min      1Q  Median      3Q     Max
-16.982  -3.196  -0.250   1.400  21.694

Coefficients:
Estimate Std. Error t value Pr(>|t|)
typeBlue M&M          17.9744    16.1923   1.110  0.27845
typeButton            21.5719    10.7832   2.001  0.05738 .
typeChoc Chip         16.9167    15.1673   1.115  0.27622
typeRed M&M           26.5760    13.1722   2.018  0.05545 .
typeSmall M&M         22.1977    29.0849   0.763  0.45310
typeSnow Cap           8.7000     9.4131   0.924  0.36495
bstime:typeBlue M&M    1.0641     0.6187   1.720  0.09887 .
bstime:typeButton      1.3352     0.3743   3.567  0.00164 **
bstime:typeChoc Chip   1.1667     0.7302   1.598  0.12373
bstime:typeRed M&M     0.5300     0.5564   0.953  0.35075
bstime:typeSmall M&M   0.1919     0.9881   0.194  0.84775
bstime:typeSnow Cap    0.9000     0.3999   2.250  0.03428 *
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

Residual standard error: 8.196 on 23 degrees of freedom
Multiple R-Squared: 0.9774,     Adjusted R-squared: 0.9656
F-statistic:  82.8 on 12 and 23 DF,  p-value: 5.616e-16

>
> and summary is:
>
>                                              Value Std.Error DF
> t-value        p-value
>      typeBlue M&M                18.0     18.5         0         0.97 NaN
>      typeButton                        21.6     14.1         0
> 1.53 NaN
>      typeChoc Chip                 16.9     17.7         0         0.96 NaN
>      typeRed M&M                26.6     16.0         0         1.66 NaN
>      typeSmall M&M              22.2     30.5         0         0.73 NaN
>      typeSnow Cap                 8.7       13.1         0         0.67 NaN
>      bstime:typeBlue M&M     1.1       0.6         24         1.72 0.098
>      bstime:typeButton             1.3       0.4         24         3.57
> 0.002
>      bstime:typeChoc Chip      1.2       0.7         24         1.60 0.123
>      bstime:typeRed M&M     0.5       0.6         24         0.95 0.350
>      bstime:typeSmall M&M   0.2      1.0          24         0.19 0.848
>      bstime:typeSnow Cap      0.9      0.4          24         2.25 0.034
>
> However in Milliken & Johnson all df are 23. Values (estimates) are
> almost identical, but there are some small differences in SE and t.
>
> Using
>
> anova(LME.1)
>
> I obtain
>
>                        numDF     denDF       F-value         p-value
> type                    6              0             18.19             NaN
> bstime:type         6            24               4.04              0.0061
>
>
> but in the book it is:
>
>
>
>                        numDF     denDF      F-value         p-value
> type                    6             23               2.00 0.1075
> bstime:type         6             23               4.04              0.0066

The tests reported by Milliken & Johnson are based on so called "Type
III" sums of squares. If you want to reproduce these, try the `Anova'
function in John Fox's indispensable `car' package.

> library(car)
> options(contrasts = c("contr.sum", "contr.poly"))
> Anova(fit, type = "III")
Anova Table (Type III tests)

Response: time
Sum Sq Df F value   Pr(>F)
type         805.13  6  1.9976 0.107510
bstime:type 1628.79  6  4.0412 0.006557 **
Residuals   1545.01 23
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

HTH,
Henric

>
> Data are at the end of the letter.
>
>
> I am not sure what I did wrong.
>
> Sincerely,
>
> Milos Zarkovic
>
>
>
> ******************************************************
> Milos Zarkovic MD, Ph.D.
> Associate Professor of Internal Medicine
> Institute of Endocrinology
> Dr Subotica 13
> Serbia
>
> Tel +381-63-202-925
> Fax +381-11-685-357
>
> Email mzarkov at eunet.yu
> ******************************************************
>
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> type,person,bstime,time
> Button,1,27,53
> Choc Chip,2,17,36
> Blue M&M,3,28,60
> Blue M&M,4,30,45
> Red M&M,5,20,30
> Choc Chip,6,29,51
> Small M&M,7,30,25
> Button,8,16,47
> Small M&M,9,32,25
> Blue M&M,10,19,38
> Blue M&M,11,33,48
> Button,12,19,39
> Snow Cap,13,15,20
> Blue M&M,14,19,34
> Choc Chip,15,20,40
> Blue M&M,16,24,42
> Snow Cap,17,21,29
> Button,18,35,90
> Red M&M,19,35,45
> Small M&M,20,30,33
> Button,21,34,65
> Button,22,40,58
> Small M&M,23,22,26
> Snow Cap,24,16,23
> Button,25,28,72
> Blue M&M,26,25,48
> Choc Chip,27,14,34
> Button,28,23,45
> Snow Cap,28,40,44
> Blue M&M,30,28,48
> Snow Cap,31,19,26
> Snow Cap,32,21,29
> Small M&M,33,32,30
> Red M&M,34,16,32
> Red M&M,35,19,47
>
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