Hello
I want to choose between two linear models describing some data in my dataset. In the field that I am studying, an independent variable, say X1, is conventionally used to predict some dependent variable, say Y1:
model 1: Y1 = a1*X1 + b
I have hypothesised that X1 is a better predictor of a different variable, say Y2
model 2: Y2 = a1*X1+b
Furthermore, I propose that if a second predictor, say X2, is taken into account, the model becomes even better
model 3: Y2 = a1*X1 + a2*X2 + b
The importance of this lies in the fact, that Y1 and Y2 are calculated measures based on some raw data. So if model 2 and 3 are shown to be better than model 1, one may prefer to calculate Y2 based on the raw data, rather than Y1 for future experiments.
Now, I know that models 2 and 3 may be compared using the Akaikes information criterion (AIC). But the core argument for me is to compare model 2 to model 1 - and importantly, compare the final model, i.e. model 3, to the reference model that is conventionally used, i.e. model 1
To compare 3 to 1, the AIC does not apply, because I am looking at different dependent variables. But any suggestions on alternative methods ?
I have limited knowledge about statistics, so please explain in simple terms and please include an example with Stata commands if possible
Thanks in advance
I want to choose between two linear models describing some data in my dataset. In the field that I am studying, an independent variable, say X1, is conventionally used to predict some dependent variable, say Y1:
model 1: Y1 = a1*X1 + b
I have hypothesised that X1 is a better predictor of a different variable, say Y2
model 2: Y2 = a1*X1+b
Furthermore, I propose that if a second predictor, say X2, is taken into account, the model becomes even better
model 3: Y2 = a1*X1 + a2*X2 + b
The importance of this lies in the fact, that Y1 and Y2 are calculated measures based on some raw data. So if model 2 and 3 are shown to be better than model 1, one may prefer to calculate Y2 based on the raw data, rather than Y1 for future experiments.
Now, I know that models 2 and 3 may be compared using the Akaikes information criterion (AIC). But the core argument for me is to compare model 2 to model 1 - and importantly, compare the final model, i.e. model 3, to the reference model that is conventionally used, i.e. model 1
To compare 3 to 1, the AIC does not apply, because I am looking at different dependent variables. But any suggestions on alternative methods ?
I have limited knowledge about statistics, so please explain in simple terms and please include an example with Stata commands if possible
Thanks in advance
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