That parameter is the difference between the estimated parameter for
the product of reflection and angleNoise in regions where reflection
was < Break(xMin) compared with the same product's parameter in those
regions of 3-space where reflection was not. In general it is at best
merely speculative (and generally rather dangerous) to interpret the
meanings of individual parameters which apply to variables that are
modeled with interactions. It is in particular a fool's errand to look
at the std errors of such parameters. Anova tables compared across
nested models are much less misleading.
You certainly _cannot_ say that there is more "importance" in the
region where reflection is < Break[min]. The parameter is measuring
differences between both regions. If you had instead constructed the
model with the reversed inequality, the parameter would have been of
the same magnitude but reverse sign and would have had the same
standard error.
It is usually much more informative to examine the predictions that
result from the models, and this may be greatly aided by plotting
across a range of values, in this case perhaps with persp() or
contour(). Dealing with three-way interactions can be particularly
messy, so I think it's fair to inquire why you are adding terms to
models when you are not prepared to interpret them? Throwing terms
into a model with no physical basis can be amusing but rarely good
science. You are the domain expert, after all. There should be a
design and rationale behind this process.
You will also note that the third and fifth of your five terms were
superfluous because all of their estimates were NA. The other three
terms covered all the possibilities, since the cases where reflection
>= Break[xMin] would be covered by their contribution to the
angleNoise*reflction (with (reflection < Break[xMin]) ==0 )
--
David (son of a son of an engineer)
On Sep 19, 2010, at 3:54 PM, zozio32 wrote:
>
> Hello, I am all new here.
> Thanks for the job done, R really helped me in my thesis lately.
> However, I
> am kind of new in statistics, coming from mecanical engineering, and I
> mostly teached myself with "The R Book", so I may do silly things
> some time.
> PLease tell me if you think so.
>
> Anyway, I've just build up a piecewise linear model to fit some data,
> including some interaction and i am not sure of how to interpret the
> summary:.
> here it is:
>
>
--------------------------------------------------------------------------------
> Call:
> lm(formula = weightedDiff ~ angleNoise +
> (reflection < Break[xMin]) * reflection +
> (reflection >= Break[xMin]) * reflection +
> angleNoise:(reflection < Break[xMin]) *
> reflection +
> angleNoise:(reflection >= Break[xMin]) *
> reflection)
>
> Residuals:
> Min 1Q Median 3Q Max
> -1.073e-03 -1.749e-04 -5.913e-06 1.650e-04 1.311e-03
>
> Coefficients: (4 not defined because of singularities)
> Estimate Std.
> Error
> (Intercept) 0.0134798
> 0.0001086
> angleNoise 0.0004658
> 0.0002245
> reflection < Break[xMin]TRUE -0.0028766
> 0.0001236
> reflection 0.0316122
> 0.0014741
> reflection >= Break[xMin]TRUE
> NA NA
> reflection < Break[xMin]TRUE:reflection 0.0683631
> 0.0027668
> reflection:reflection >= Break[xMin]TRUE
> NA NA
> angleNoise:reflection < Break[xMin]TRUE 0.0011158
> 0.0002548
> angleNoise:reflection >= Break[xMin]TRUE
> NA NA
> angleNoise:reflection < Break[xMin]FALSE:reflection -0.0055751
> 0.0030620
> angleNoise:reflection < Break[xMin]TRUE:reflection -0.0343745
> 0.0049164
> angleNoise:reflection:reflection >= Break[xMin]TRUE
> NA NA
>
> t value Pr(>|t|)
> (Intercept)
> 124.079 < 2e-16 ***
> angleNoise
> 2.075 0.0384 *
> reflection < Break[xMin]TRUE
> -23.265 < 2e-16 ***
> reflection
> 21.445 < 2e-16 ***
> reflection >= Break[xMin]TRUE
> NA NA
> reflection < Break[xMin]TRUE:reflection
> 24.708 < 2e-16 ***
> reflection:reflection >=
> Break[xMin]TRUE NA
> NA
> angleNoise:reflection < Break[xMin]TRUE
> 4.379
> 1.41e-05 ***
> angleNoise:reflection >= Break[xMin]TRUE NA
> NA
> angleNoise:reflection < Break[xMin]FALSE:reflection -1.821
> 0.0692 .
> angleNoise:reflection < Break[xMin]TRUE:reflection -6.992
> 7.35e-12 ***
> angleNoise:reflection:reflection >= Break[xMin]TRUE NA
> NA
> ---
> Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
>
> Residual standard error: 0.0002885 on 592 degrees of freedom
> Multiple R-squared: 0.9666, Adjusted R-squared: 0.9662
> F-statistic: 2450 on 7 and 592 DF, p-value: < 2.2e-16
>
>
--------------------------------------------------------------------------------------------
> Basically, I am really not sure of the meaning of this parameter:
> angleNoise:reflection < Break[xMin]FALSE:reflection
>
> Overall, my interpretation is that reflection is important , angle
> Noise
> also but specially when reflection is below the breaking point. Is
> that
> correct?
>
> well, sorry for the first long post
>
> thanks in advance
>
> --
> View this message in context:
http://r.789695.n4.nabble.com/help-interpreting-a-model-summary-tp2546161p2546161.html
> Sent from the R help mailing list archive at Nabble.com.
>
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