[R] Interpretation of gam intercept parameter

[Lidia Dobria]

Gavin,
 
Thank you for your clear explanation. I'm just learning R, hence my not knowing how to dummy code a variable using R. Your example was very useful!

Thank you again.
Lidia

----------------------------------------
> Subject: Re: [R] Interpretation of gam intercept parameter
> From: gavin.simpson at ucl.ac.uk
> To: lidiadobria at hotmail.com
> CC: r-help at r-project.org
> Date: Wed, 30 Jun 2010 08:31:45 +0100
>
> On Tue, 2010-06-29 at 21:27 -0500, Lidia Dobria wrote:
>> Dear All:
>>
>> I apologize for asking such an elementary question, but I could not
>> find an adequate response on line. I am hoping to receive some help
>> with the interpretation of the Intercept coefficient in the gam model
>> below.
>>
>> I1 through I3 are dummy coded "Item difficulty" parameters in a data
>> set that includes 4 items. If the Intercept is the value of Y when all
>> other terms are 0, am I correct in assuming that it also equals the
>> difficulty of item 4 (dummy coded 0 0 0 )?
>
> If I understand you correctly (?) you have a single variable 'ID' (Item
> Difficulty) taking three levels 1,2,3. If so, you should avoid making
> your dummy variables by hand and let R's formula handling sugar take
> care of this for you.
>
> fac <- factor(sample(rep(letters[1:3], each = 4)))
> resp <- rnorm(12)
> num <- rnorm(12)
> model.matrix(resp ~ fac + num)
>
> (Intercept) facb facc num
> 1 1 0 1 1.22373197
> 2 1 0 0 -0.23893032
> 3 1 1 0 -0.03588385
> 4 1 1 0 0.39657910
> 5 1 0 1 0.14727398
> 6 1 1 0 0.59727570
> 7 1 0 1 -0.24968044
> 8 1 0 0 0.01444002
> 9 1 0 1 0.45514437
> 10 1 1 0 -0.74748326
> 11 1 0 0 0.89873549
> 12 1 0 0 1.37584734
> attr(,"assign")
> [1] 0 1 1 2
> attr(,"contrasts")
> attr(,"contrasts")$fac
> [1] "contr.treatment"
>
> With treatment contrasts the intercept is the mean for the reference
> level (which is the first entry in levels(fac) ) and the facb and facc
> entries above code for the difference in the mean response of the b and
> c groups from the reference level mean (group a). To parametrise on the
> group means, suppress the intercept
>
> model.matrix(resp ~ 0 + fac + num) ## or
> model.matrix(resp ~ fac + num - 1)
>
> This all happens within the model fitting code, so I could run gam as:
>
> require(mgcv)
> ## Probably good idea to have you data in a data frame
> dat <- data.frame(fac, resp, num)
> rm(resp, num, fac)
> mod <- gam(resp ~ fac + s(num), data = dat)
> summary(mod)
> anova(mod)
>
> Compare the summary() and anova() output; in the former the data is at
> the level of each coefficient (the treatment contrast info I mention
> above), whilst in anova() the single term for fac combines this
> information into a single value for the entire term 'fac'.
>
> If you want to alter the contrasts, look at ?contrasts
>
> Does it help if you recode your model using R's tools?
>
> G
>
>>
>> Thank you for your help.
>> Lidia
>>
>>
>> Family: gaussian
>> Link function: identity
>>
>> Formula:
>> Score ~ I1 + I2 + I3 + s(TimeI1, bs = "cr", k = 7) +
>> s(TimeI2, bs = "cr", k = 7) + s(TimeI3, bs = "cr", k = 7)
>>
>> Parametric coefficients:
>> Estimate Std. Error t value Pr(>|t|)
>> (Intercept) 4.70968 0.09547 49.330 < 2e-16 ***
>> I1 -0.22188 0.21767 -1.019 0.308157
>> I2 0.51236 0.16592 3.088 0.002042 **
>> I3 -0.60697 0.18258 -3.324 0.000902 ***
>> ---
>> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>>
>> Approximate significance of smooth terms:
>> edf Ref.df F p-value
>> s(TimeI1) 3.820 3.820 4.587 0.001331 **
>> s(TimeI2) 2.491 2.491 6.271 0.000784 ***
>> s(TimeI3) 3.481 3.481 8.997 1.54e-06 ***
>> ---
>>
>> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>> R-sq.(adj) = 0.057 Scale est. = 2.131 n = 2079
>> ______________________________________________
>> 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.
>
> --
> %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%
> Dr. Gavin Simpson [t] +44 (0)20 7679 0522
> ECRC, UCL Geography, [f] +44 (0)20 7679 0565
> Pearson Building, [e] gavin.simpsonATNOSPAMucl.ac.uk
> Gower Street, London [w] http://www.ucl.ac.uk/~ucfagls/
> UK. WC1E 6BT. [w] http://www.freshwaters.org.uk
> %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%
>