[R] ANCOVA: Next steps??

[Prof Brian Ripley]

On Sat, 16 Aug 2008, Brown, Heidi wrote:

> Having spent the last few weeks trying to decipher R, I feel I may 
> finally be getting somewhere, but i'M still in need of some advice and 
> all my tutors seem to be on holiday!
>
> Basically a bit of background, I have data collected on a population of 
> Lizards which includes age,sex, and body condition. I collected data 
> myself this year and I have data previously collected from 1999, 2002 
> and 2005. My plan is to compare this data to identify if there has been 
> any change in body condition since the first sample in 1999. I have run 
> my data through R using the following:

What is 'year'?  I am wondering if it should have been a factor.  If it 
has been entered as numeric the results are relative to year dot (0) and 
the intercept is meaningless.

You mention ANCOVA here but I see no {C}ovariates (unless you have good 
reason to treat 'year' as numeric), and you do not even show an ANOVA 
table.  Take a look at MASS (the book) chapter 6 and use step() or similar 
to do backwards model selection following its examples. In particular you 
need to respect the hierarchy of terms, so you can only remove 
age:sex:year at the first stage.

This sort of thing is best done in an interactive consultation with a 
statistician (or a biologist with MSc-level statistical training): until 
the full model properly reflects the design the R output presented is not 
useful.


>
> mos1<-lm(ci~age*sex*year)
> summary(mos1)
>
> and R has gven me the results
>
> Call:
> lm(formula = ci ~ age * sex * year)
> Residuals:
>      Min        1Q    Median        3Q       Max
> -0.156304 -0.036740  0.002953  0.039081  0.213696
> Coefficients:
>                 Estimate Std. Error t value Pr(>|t|)
> (Intercept)      9.538260   4.956850   1.924   0.0556 .
> ageJ           -15.943787  11.211551  -1.422   0.1564
> sexM           -11.844042   6.195258  -1.912   0.0572 .
> year            -0.004657   0.002474  -1.883   0.0611 .
> ageJ:sexM       18.887391  13.657536   1.383   0.1681
> ageJ:year        0.007923   0.005590   1.417   0.1578
> sexM:year        0.005977   0.003091   1.934   0.0545 .
> ageJ:sexM:year  -0.009458   0.006809  -1.389   0.1663
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> Residual standard error: 0.06299 on 218 degrees of freedom
> Multiple R-squared: 0.6109,     Adjusted R-squared: 0.5984
> F-statistic: 48.89 on 7 and 218 DF,  p-value: < 2.2e-16
>
> Firstly I'm a bit bemused, I think my head has turned to mush the last 
> few weeks and I'm struggling to decipher the results, am I right in 
> thinking the intercept Adult Females?? and secondly I have Been told to 
> update the model to produce the minimal adequate model. By doing this do 
> I need to remove the least significant from the above list ie age:sex:?
>
> mos2<-update(mos1,~.-age:sex)
> summary(mos2)
>
> Call:
> lm(formula = ci ~ age + sex + year + age:year + sex:year + age:sex:year)
> Residuals:
>      Min        1Q    Median        3Q       Max
> -0.161296 -0.040699  0.001092  0.038537  0.208704
> Coefficients:
>                 Estimate Std. Error t value Pr(>|t|)
> (Intercept)     7.050e+00  4.628e+00   1.523    0.129
> ageJ           -3.216e+00  6.416e+00  -0.501    0.617
> sexM           -7.958e+00  5.533e+00  -1.438    0.152
> year           -3.416e-03  2.310e-03  -1.479    0.141
> ageJ:year       1.577e-03  3.199e-03   0.493    0.622
> sexM:year       4.038e-03  2.761e-03   1.463    0.145
> ageJ:sexM:year -4.132e-05  9.762e-06  -4.233 3.40e-05 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> Residual standard error: 0.06312 on 219 degrees of freedom
> Multiple R-squared: 0.6075,     Adjusted R-squared: 0.5967
> F-statistic: 56.49 on 6 and 219 DF,  p-value: < 2.2e-16
>
> Basically how do i know once the minimal adequate model has been 
> reached? how many times should I remove categories and update the model?
>
> Any help will be greatly appreciated and if more information is required 
> then let me know!!
>
> Cheers
>
> H
>
>
>
>
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595