[R] Interpreting factor*numeric interaction coefficients

[ONKELINX, Thierry]

Dear Matthew,

The easiest way the get the estimates (and their standard error) for the
different slopes it to reparametrise your model. Use resp ~ var1 : cat +
0 instead of resp ~ var1 * cat

HTH,

Thierry

------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek
team Biometrie & Kwaliteitszorg
Gaverstraat 4
9500 Geraardsbergen
Belgium

Research Institute for Nature and Forest
team Biometrics & Quality Assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium

tel. + 32 54/436 185
Thierry.Onkelinx op inbo.be
www.inbo.be

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say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

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ensure that a reasonable answer can be extracted from a given body of
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> -----Oorspronkelijk bericht-----
> Van: r-help-bounces op r-project.org 
> [mailto:r-help-bounces op r-project.org] Namens Matthew Carroll
> Verzonden: maandag 12 april 2010 11:16
> Aan: r-help op r-project.org
> Onderwerp: [R] Interpreting factor*numeric interaction coefficients
> 
> Dear all,
> I am a relative novice with R, so please forgive any terrible 
> errors...
> 
> I am working with a GLM that describes a response variable as 
> a function of a categorical variable with three levels and a 
> continuous variable. These two predictor variables are 
> believed to interact.
> An example of such a model follows at the bottom of this 
> message, but here is a section of its summary table:
> 
>                    Estimate	Std. Error z value Pr(>|z|)  
> (Intercept)        1.220186  	0.539475   2.262   0.0237 *
> var1               0.028182  	0.050850   0.554   0.5794  
> cat2               -0.112454  0.781137  -0.144   0.8855  
> cat3               0.339589   0.672828   0.505   0.6138  
> var1:cat2          0.007091   0.068072   0.104   0.9170  
> var1:cat3          -0.027248  0.064468  -0.423   0.6725  
> 
> I am having trouble interpreting this output.
> I think I understand that:
> 
> # the 'var1' value refers to the slope of the relationship 
> within the first factor level
> 
> # the 'cat2' and 'cat3' values refer to the difference in 
> intercept from 'cat1'
> 
> # the interaction terms describe the difference in slope 
> between the relationship in 'cat1' and that in 'cat2' and 
> 'cat3' respectively
> 
> Therefore, if I wanted a single value to describe the slope 
> in either cat2 or cat3, I would sum the interaction value 
> with that of var1.
> 
> However, if I wanted to report a standard error for the slope 
> in 'cat2', how would I go about doing this? Is the reported 
> standard error that for the overall slope for that factor 
> level, or is the actual standard error a function of the 
> standard error of var1 and that of the interaction?
> 
> Any help with this would be much appreciated,
> 
> Matthew Carroll
> 
> 
> ### example code
> 
> resp <- rpois(30, 5)
> cat <- factor(rep(c(1:3), 10))
> var1 <- rnorm(30, 10, 3)
> 
> mod <- glm(resp ~ var1 * cat, family="poisson")
> summary(mod)
> 
> Call:
> glm(formula = resp ~ var1 * cat, family = "poisson")
> 
> Deviance Residuals: 
>      Min        1Q    Median        3Q       Max  
> -1.80269  -0.54107  -0.06169   0.51819   1.58169  
> 
> Coefficients:
>                    Estimate	Std. Error z value Pr(>|z|)  
> (Intercept)        1.220186  	0.539475   2.262   0.0237 *
> var1               0.028182  	0.050850   0.554   0.5794  
> cat2               -0.112454  0.781137  -0.144   0.8855  
> cat3               0.339589   0.672828   0.505   0.6138  
> var1:cat2          0.007091   0.068072   0.104   0.9170  
> var1:cat3          -0.027248  0.064468  -0.423   0.6725  
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
> (Dispersion parameter for poisson family taken to be 1)
> 
>     Null deviance: 23.222  on 29  degrees of freedom Residual 
> deviance:
> 22.192  on 24  degrees of freedom
> AIC: 133.75
> 
> Number of Fisher Scoring iterations: 5
> 
> 
> 
> --
> Matthew Carroll
> E-mail: mjc510 op york.ac.uk
> 
> ______________________________________________
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> 

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