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I am comparing two different models (multiple linear model).

Basically the explanatory variables remain the same while response variable are different.

$Model\ 1 - Y_1 = X_1+X_2+X_3$

$Model\ 2 - Y_2 = X_1+X_2+X_3$

I have results from R for both models.

I am just wondering if two of these results eg $F$-statistics, $p$-value, $R^2$, RSS are comparable. So can I say model 1 is better because p-value is smaller. etc ?

From what I learned from class, I only compared models which had the same response variable and different explanatory variables.

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  • $\begingroup$ Have a look at the following posts, maybe they are helpful: first, second, third. $\endgroup$
    – COOLSerdash
    Commented Jun 6, 2013 at 16:33
  • $\begingroup$ Is there a functional relationship between $Y_1$ and $Y_2$, ie, can we write $Y_1=g(Y_2)$? Or merely a stochastic relationship ($Y_1 = g(Y_2) +$ error)? $\endgroup$
    – Andrew M
    Commented Oct 9, 2014 at 17:30
  • $\begingroup$ If $Y_1$ and $Y_2$ are both measuring the same kind of variable in the same units, so that the coefficients in the two equations are measuring the same thing, the coefficients can be compared (indeed a CI for their difference can be generated, for example). However, in that case it's more common to combine the two into a single equation and add a dummy variable for the data set (which main effect picks up difference in intercept), whose interactions can be used to pick up differences in slope coefficients. $\endgroup$
    – Glen_b
    Commented Nov 11, 2014 at 22:28

1 Answer 1

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Yes, you can only really compare two models with the same dependent variable for an F-test. How similar are the two dependent variables? Are they the same outcome from different samples? Or are they two very separate responses?

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  • $\begingroup$ One response variable is total volume and another one is the partial volume. So they are very correlated. $\endgroup$
    – user1925750
    Commented Jun 6, 2013 at 15:29
  • $\begingroup$ They have similar distributions but not exactly the same. Perhaps, I can compare them ? What do you think? $\endgroup$
    – user1925750
    Commented Jun 6, 2013 at 15:32
  • $\begingroup$ user1925750, what would it mean to compare them? What does it actually tell you? $\endgroup$
    – Glen_b
    Commented Aug 6, 2013 at 1:24
  • $\begingroup$ I think what Glen_b means is that testing a difference will likely only tell you that there is a difference. But, it doesn't make sense to even do the test because this particular test strictly needs the same dependent variable. $\endgroup$
    – Francisco Arceo
    Commented Aug 6, 2013 at 15:15

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