[R] Ancova_non-normality of errors

[John Fox]

Dear Tobias,

Your observation that "When plot [the residuals from?] this model I get a
banana-shape in Normal Q-Q Plot(with open site [side?] pointing downwards),"
suggests that the residuals are negatively skewed, which in turn suggests
that using log(wt) as the response variable may have been ill-advised.
Perhaps simply using wt, or a weaker transformation such as sqrt(wt), would
produce better-behaved residuals.

I hope this helps,
 John 

------------------------------
John Fox, Professor
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
web: socserv.mcmaster.ca/jfox


> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
> Behalf Of Tobias Erik Reiners
> Sent: May-04-08 5:56 AM
> To: r-help at r-project.org
> Subject: [R] Ancova_non-normality of errors
> 
> Hello Helpers,
> 
> I have some problems with fitting the model for my data...
> -->my Literatur says (crawley testbook)=
> Non-normality of errors-->I get a banana shape Q-Q plot with opening
> of banana downwards
> 
> Structure of data:
>       origin   wt   pes gender
> 1      wild 5.35 147.0   male
> 2      wild 5.90 148.0   male
> 3      wild 6.00 156.0   male
> 4      wild 7.50 157.0   male
> 5      wild 5.90 148.0   male
> 6      wild 5.95 148.0   male
> 7      wild 8.55 160.5   male
> 8      wild 5.90 148.0   male
> 9      wild 8.45 161.0   male
> 10     wild 4.90 147.0   male
> 11     wild 6.80 153.0   male
> 12     wild 5.75 146.0   male
> 13     wild 8.60 160.0   male
> 14  captive 6.85 159.0   male
> 15  captive 7.00 160.0   male
> 16  captive 6.80 155.0   male
> ..
> ...
> 283    site 4.10 130.4 female
> 284    site 3.55 131.1 female
> 285    site 4.20 135.7 female
> 286    site 3.45 128.0 female
> 287    site 3.65 125.3 female
> 
> The goal of my analysis is to work out what effect the categorial
> factors(origin, gender) on the relation between
> log(wt)~log(pes)(-->Condition, fett ressource), have.
> Does the source(origin) of translocated animals have an affect on
> performance(condition)in the new area?
> I have already a best fit model and it looks quite good (or not?see
below).
> 
> two slopes(gender difference)and 6 intercepts(3origin levels*2gender
levels)
> 
> lm(formula = log(wt) ~ log(pes) + origin + gender + gender:log(pes))
> 
> Residuals:
>       Min       1Q   Median       3Q      Max
> -0.54181 -0.07671  0.01520  0.09474  0.28818
> 
> Coefficients:
>                      Estimate Std. Error t value Pr(>|t|)
> (Intercept)         -7.39879    1.97605  -3.744 0.000219 ***
> log(pes)             1.78020    0.40118   4.437 1.31e-05 ***
> originsite           0.06572    0.01935   3.397 0.000781 ***
> originwild           0.07655    0.03552   2.155 0.032011 *
> gendermale          -9.32418    2.37476  -3.926 0.000109 ***
> log(pes):gendermale  1.90393    0.47933   3.972 9.06e-05 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> Residual standard error: 0.1433 on 281 degrees of freedom
> Multiple R-Squared: 0.7227,     Adjusted R-squared: 0.7177
> F-statistic: 146.4 on 5 and 281 DF,  p-value: < 2.2e-16
> 
> When plot this model I get a banana-shape in Normal Q-Q Plot(with open
> site pointing downwards) , indicating non-normality of my data....how
> to handle this?
> 
> -->Do I have unbalanced data?
>        captive    site    wild
> n-->     119     149      19
> 
> My problem is that I see that my data is not as good as the
> modelsummary tells.
> Should I include another term in my model formular?
> 
> I think I have to differenciate more, but I don't know
> how.(contrasts?, TukeyHSD?,Akaike Information Criterion? or lme())to
> many different ways out there.
> 
> Cheers,
> Tobi
> 
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