ベータ回帰から係数を解釈する方法は？

0〜1の範囲のデータがありますbetareg。R のパッケージを使用して、制限されたデータを従属変数として回帰モデルに適合させました。私の質問は、回帰の係数をどのように解釈すればよいですか？

このpdfを読んでください：cran.r-project.org/web/packages/betareg/vignettes/betareg.pdf あなたの質問に答えるべき多くの有用な例。

おかげで、pdfを見ていたが、私はまだ係数を解釈する方法がわからない

— トーマスジェンセン

問題ない。以下に回答を掲載します。

そのため、応答をモデル化するスケールを把握する必要があります。betaregR の関数の場合、次のモデルがあります

logit (y_{i}) = β_{0} + \sum_{i = 1}^{p} β_{i}

$\text{logit}(y_i)=\beta_0+\sum_{i=1}^p\beta_i$

$\text{logit}(y_i)$ glmbetareg

logit (y_{i}) = β_{0} + \sum_{i = 1}^{p} β_{i} \Rightarrow y_{i} = \frac{e^{β_{0} + \sum_{i = 1}^{p} β_{i}}}{1 + e^{β_{0} + \sum_{i = 1}^{p} β_{i}}}

$\text{logit}(y_i)=\beta_0+\sum_{i=1}^p\beta_i\Rightarrow y_i=\frac{e^{\beta_0+\sum_{i=1}^p\beta_i}}{1+e^{\beta_0+\sum_{i=1}^p\beta_i}}$

Thus you should realize that we are basically using the same results and interpretations from standard generalized linear modeling (under the logit link). One of the main differences between logistic regression and beta regression is that you are allowing the variance of your response to be much larger than it could be in logistic regression in order to deal with the typical problem of over-dispersion.

— Nick Cox
ソース

Awesome, much appreciated!!

— Thomas Jensen

@Nick Cox Nick so when if you had a proportional response that was a proportion of species observed and a independent variable TEMPERATURE . My confusion with a betareg is what the coefficient indicates an increase of ....the odds of what? In a typical logistic regression because the outcome is categorical I get intuitively that ther is increase in odds of being in a category BUT with continuous proportion outcome how can you explain an increase with odds? If the temperature coef is .05 so exp(.05) = 1.05 that would say a one unit increase in temp leads to a 1.05 increase in what?

— user3022875

@user3022875 In the example you give, it represents an increase in the ratio of proportion species observed to proportion of species not observed. The odds is just the ratio between positive and negative classes (p/1-p), so rather than saying "odds" you can just describe the ratio explicitly.

— Bryan Shalloway

so in the example from user3022875 the interpretation would be: one unit increase in temp leads to 5% increase in the ratio of proportion species observed to proportion of species not observed. or simply, one unit increase in temp leads to 5% increase in the ratio of proportion species observed. is that right, @BryanShalloway?

— user1607