From: Frank E Harrell Jr <f.harrell_at_vanderbilt.edu>

Date: Tue, 15 Jul 2008 20:25:22 -0500

Date: Tue, 15 Jul 2008 20:25:22 -0500

Dylan Beaudette 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?
*

No

*>
*

> Compared to the above example, what tests are performed when calling

*> anova() on this object? Here is the output in R:
*

Mark Difford gave a nice response for that.

Frank

*>
*

> 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
**> 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.
**>
*

-- Frank E Harrell Jr Professor and Chair School of Medicine Department of Biostatistics Vanderbilt University ______________________________________________ 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.Received on Wed 16 Jul 2008 - 01:29:06 GMT

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.2.0, at Wed 16 Jul 2008 - 04:32:02 GMT.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help.
Please read the posting
guide before posting to the list.
*