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

[Mark Difford]

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
> 
> ______________________________________________
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> 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.
> 
> 

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