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I am having difficulty interpreting the significance of positive tone (measured as percentage of words in a sentence that are positive in tone) for females and males. The following is the regression estimate for the log-transformed dependent variable.

log(DaysToOutcome)=-0.12 -0.32*Female + 0.02*PositiveTone +0.03*NegativeTone -0.04*Female:PositiveTone -0.03*Female:NegativeTone.

How do I estimate what one percentage point change in positive tone would result in terms of percentage change in outcome variable for females and males? Please help!

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Let $X$ = positive tone percent, $Z$ = negative tone percent, $Y$ = daystooutcome. For male with $X = x$, $log(Y|x) = -0.12 +0.02x +0.03Z$. For male with $X=x+1$ (one percentage point change), $log(Y|x+1) = -0.12 +0.02(x+1) +0.03Z$. So $log(Y|x+1) - log(Y|x) = log\left(\frac {Y|x+1}{Y|x}\right) = 0.02$. So $\frac {Y|x+1}{Y|x} = e^{0.02}$ for male.

For female, we have $log(Y|x) = -0.12 -0.32 + 0.02x - 0.03Z -0.04x$.

$log(Y|x+1) = -0.12 -0.32 + 0.02(x+1) - 0.03Z -0.04(x+1)$.

$log(Y|x+1) - log(Y|x) = log\left(\frac {Y|x+1}{Y|x}\right) = 0.02 - 0.04 = -0.02$.

$\frac {Y|x+1}{Y|x} = e^{-0.02}$ for female.

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  • $\begingroup$ Thanks a lot @a_statistician!! Would that mean for females 1 percent increase in X (i.e., PositiveTone) would lead to (exp(-0.02)-1)*100 change in Y (i.e., DaysToOutcome)? $\endgroup$
    – SanMelkote
    Commented Oct 17, 2018 at 2:44
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    $\begingroup$ I think you should understand what $\frac {Y|x+1}{Y|x} = e^{-0.02} = 0.98$ means. The rest is language issue. It is really beyond my ability. $\endgroup$
    – user158565
    Commented Oct 17, 2018 at 2:51
  • $\begingroup$ Also another clarification, would a 50 percent increase in positive tone, mean (exp(50*-0.02)-1)*100 percent change in days to outcome for females? Am I getting this correct? Please correct me if I am wrong. $\endgroup$
    – SanMelkote
    Commented Oct 17, 2018 at 2:51
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    $\begingroup$ One question for you: when you fit model, if positive tone percent is 10%, you used 10 or 0.10? If you used 10, then everything we discussed are OK. If you used 0.10, we need to recalculate them. $\endgroup$
    – user158565
    Commented Oct 17, 2018 at 2:56
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    $\begingroup$ $\frac {Y|x+50}{Y|x} = e^{-0.02*50} = e^{-1} = 0.3679$ for female with a 50 percent increase in positive tone. $\endgroup$
    – user158565
    Commented Oct 17, 2018 at 3:01

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