Re: [R] meaning of tests presented in anova(ols(...)) {Design package}

From: Mark Difford <mark_difford_at_yahoo.co.uk>
Date: Tue, 15 Jul 2008 02:24:03 -0700 (PDT)

Hi Dylan,

>> I am curious about how to interpret the table produced by >> anova(ols(...)), from the Design package.

Frank will perhaps come in with more detail, but if he doesn't then you can get an understanding of what's being tested by doing the following on the saved object from your OLS call (see ?anova.Design):

print(anova(ols$obj), which="sub")
plot(anova(ols$obj))

HTH, Mark.

Dylan Beaudette-2 wrote:
>
> Hi,
>
> I am curious about how to interpret the table produced by
> anova(ols(...)), from the Design package. I have a multiple linear
> regression model, with some interaction, defined by:
>
> ols(formula = log(ksat * 60 * 60) ~ log(sar) * pol(activity,
> 3) + log(conc) * pol(sand, 3), data = sm.clean, x = TRUE,
> y = TRUE)
>
> n Model L.R. d.f. R2 Sigma
> 1834 1203 14 0.48 1.2
>
> Residuals:
> Min 1Q Median 3Q Max
> -5.033 -0.859 0.016 0.739 4.868
>
> Coefficients:
> Value Std. Error t Pr(>|t|)
> Intercept 11.3886790 2.0220171 5.63 0.0000000205580
> sar -4.3991263 1.0157588 -4.33 0.0000156609226
> activity -40.0591221 5.6907822 -7.04 0.0000000000027
> activity^2 33.0570116 5.0578520 6.54 0.0000000000819
> activity^3 -8.1645147 1.3750370 -5.94 0.0000000034548
> conc 0.3841260 0.0813200 4.72 0.0000024942478
> sand -0.0096212 0.0327415 -0.29 0.7689032898947
> sand^2 0.0008495 0.0008589 0.99 0.3227487169683
> sand^3 0.0000025 0.0000066 0.39 0.6994987342042
> sar * activity 12.8134698 2.9513942 4.34 0.0000149300007
> sar * activity^2 -9.9981381 2.6310765 -3.80 0.0001494462966
> sar * activity^3 2.1481278 0.7168339 3.00 0.0027662261037
> conc * sand -0.0157426 0.0076013 -2.07 0.0384966958735
> conc * sand^2 0.0003419 0.0001989 1.72 0.0857381555491
> conc * sand^3 -0.0000027 0.0000015 -1.77 0.0777025949762
>
>
> Looking at what I 'think' are "marginal p-values" i.e. results of a
> test against coef_i != 0, there are several terms with non-significant
> coefficients (at p<0.05). Does a non-significant coefficient warrant
> removal from the model, or perhaps a mention in the discussion?
>
> Compared to the above example, what tests are performed when calling
> anova() on this object? Here is the output in R:

>
> Analysis of Variance Response: log(ksat * 60 * 60)
>
> Factor d.f. Partial SS MS F
> sar (Factor+Higher Order Factors) 4 168.43 42.11
> 27.0
> All Interactions 3 142.13 47.38
> 30.4
> activity (Factor+Higher Order Factors) 6 536.84 89.47
> 57.3
> All Interactions 3 142.13 47.38
> 30.4
> Nonlinear (Factor+Higher Order Factors) 4 257.25 64.31
> 41.2
> conc (Factor+Higher Order Factors) 4 443.02 110.75
> 71.0
> All Interactions 3 76.74 25.58
> 16.4
> sand (Factor+Higher Order Factors) 6 1906.29 317.71
> 203.6
> All Interactions 3 76.74 25.58
> 16.4
> Nonlinear (Factor+Higher Order Factors) 4 263.00 65.75
> 42.1
> sar * activity (Factor+Higher Order Factors) 3 142.13 47.38
> 30.4
> Nonlinear 2 95.32 47.66
> 30.5
> Nonlinear Interaction : f(A,B) vs. AB 2 95.32 47.66
> 30.5
> conc * sand (Factor+Higher Order Factors) 3 76.74 25.58
> 16.4
> Nonlinear 2 4.98 2.49
> 1.6
> Nonlinear Interaction : f(A,B) vs. AB 2 4.98 2.49
> 1.6
> TOTAL NONLINEAR 8 455.20 56.90
> 36.5
> TOTAL INTERACTION 6 218.87 36.48
> 23.4
> TOTAL NONLINEAR + INTERACTION 10 573.36 57.34
> 36.7
> REGRESSION 14 2631.53 187.97
> 120.4
> ERROR 1819 2839.25 1.56
> P
> <.0001
> <.0001
> <.0001
> <.0001
> <.0001
> <.0001
> <.0001
> <.0001
> <.0001
> <.0001
> <.0001
> <.0001
> <.0001
> <.0001
> 0.203
> 0.203
> <.0001
> <.0001
> <.0001
> <.0001
>
> Are more of the 'terms' significant (at p<0.05) due to pooling of
> model terms? I have looked through Frank's book on the topic, but
> can't quite wrap my head around what the above is telling me. I am
> mostly interested in presenting a model for use as a applied tool, and
> interpretation of terms / interaction is very important.
>
> Thanks,
>
> Dylan
>
> ______________________________________________
> R-help_at_r-project.org mailing list
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> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
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>
>

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