生態学のデータ解析 - summary(glm()) の星

• R の glm() の summary の係数の推定値の表 (table of coefficients) について

  

• 参照: FAQ 一般化線形モデル, GLM 参照

(まだ書きかけです)

[項目]

• 「星」がつく? つかない?
• show.signif.stars の設定
• R-help 上での議論

「星」がつく? つかない? 

• glm() の推定結果を summary() すると係数 (coefficieints) の推定値に関する table が表示されます．

Call:
glm(formula = y ~ x + f, family = poisson, data = d)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.3978  -0.7337  -0.2023   0.6795   2.4317  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)  1.26311    0.36963   3.417 0.000633 ***
x            0.08007    0.03704   2.162 0.030620 *  
fT          -0.03200    0.07438  -0.430 0.667035    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

(Dispersion parameter for poisson family taken to be 1)

• ただし R のオプション指定で， show.signif.stars が FALSE になっていると， 「星」は表示されません．

Call:
glm(formula = y ~ x + f, family = poisson, data = d)

Deviance Residuals: 
   Min      1Q  Median      3Q     Max  
-2.398  -0.734  -0.202   0.679   2.432  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)   1.2631     0.3696    3.42  0.00063
x             0.0801     0.0370    2.16  0.03062
fT           -0.0320     0.0744   -0.43  0.66703

(Dispersion parameter for poisson family taken to be 1)

• show.signif.stars 設定が影響する関数
• summary.glm() を表示する print.summary.glm() (関数は getS3method("print", "summary.glm") で表示できる --- 参照 methods(print))
• 係数の table を表示する printCoefmat() 関数

show.signif.stars の設定 

• show.signif.stars はどう設定するか?
  • options(show.signif.stars = FALSE) (参照 help(options))
  • あるいは Rprofile ファイルに options(show.signif.stars = FALSE)

R-help 上での議論 

• 係数の推定値に "significancy" に関連して，show.signif.stargs をデフォルトで FALSE にすべきでは? といった議論が R-help であった (2000 年 9 月ごろ)
  • https://stat.ethz.ch/pipermail/r-help/2000-September/thread.html#8390 から始まる議論
    • Thread が途中でつけかわってますが

• 久保が気に入ったコメント，いくつか (かきかけ)
• JAGS を作った Martin Plummer さん (https://stat.ethz.ch/pipermail/r-help/2000-September/008396.html)

I would hope that you never conduct an analysis without knowing what the variables mean!

• MASS 本 の著者のひとり Bill Venables さん (https://stat.ethz.ch/pipermail/r-help/2000-September/008400.html)

I accept full responsibilty... and I am sticking to my guns. I think this is a crucial point of inference often misunderstood. It is at the core of the reason why putting significance stars routinely on t-statistics is NOT a good idea - by doing so you encourage confusion and unjustified inferences.

Let me start to answer by asking you "What does a `significant' t-test result mean?" To me it means that if someone were to pose the null hypothesis that the mean (or in this case regression coefficient) were zero, you would have, by convention, strong enough evidence to reject it. If the result were `non-significant', by contrast, it does NOT allow you to assert that the regression coefficient IS zero, it only means that you do not have enough EVIDENCE to reject such a claim. The real question is whether or not it is a claim anyone would have good reason to make in the first place - sometimes it would be, sometimes not. In the case above I would say from the context there is no good reason for anyone a priori to claim that the derivative at temperature 0 should be zero, that is, that the curve should necessarily be flat at that rather arbitrary point.

• MASS 本のもうひとりの著者，Brian Ripley 御大の ないす なコメント (show.signif.stars が default で TRUE になっていることに関して; https://stat.ethz.ch/pipermail/r-help/2000-September/008446.html)

I always forget that that they are turned on by default, for I have

	auk% cat ~/.Rprofile
	options(show.signif.stars=FALSE)
	ps.options(horizontal=FALSE)
			

and so never see them.