Take the 2-minute tour ×
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It's 100% free, no registration required.

I have a dependent variable $Y$, an independent variable $X$, and a categorical independent variable T (which can take 2 levels). Now I have 4 models:

MI: different slopes, different intercepts $$y_{i1}=\alpha_1+\beta_1x_{i1}, y_{i2}=\alpha_2+\beta_2x_{i2}; \text{or}\; y_{ij}=\beta_0+\beta_1X_{ij}+\beta_2T_i+\beta_3X_{ij}T_j$$

MII: same slope, different intercepts $$y_{i1}=\alpha_1+\beta x_{i1}, y_{i2}=\alpha_2+\beta x_{i2}; \text{or}\; y_{ij}=\beta_0+\beta_1X_{ij}+\beta_2T_j$$

MIII: same intercept, different slopes $$y_{i1}=\alpha+\beta_1x_{i1}, y_{i2}=\alpha+\beta_2x_{i2}$$

MIV: one regression line for both $$y_{ij}=\alpha+\beta x_{ij}; \text{or}\; y_{ij}=\beta_0+\beta_1X_i$$

Now I am trying to compare these models one against the other. I am not sure, if I am right with what I think:
Comparing MI to MII tests $H_0:\, \beta_1=\beta_2$ (this I do know), which means that $H_0$: same slope against $H_a$: different slopes (which I am not sure of). If I compare these in R, I get a p-value. Now what I think is that, if the p-value < alpha level, I can reject $H_0$, which would mean I should stick to the first model. If it is a large value, I cannot reject the null hypotheses, which means I should stick with the second model (as there I have the same slope). I am not sure if I am right with that.
Plus I cannot write down the second equation for the model third model, can someone help out?

share|improve this question
add comment

1 Answer 1

MIII could be written $y_{ij} = \beta_0 + \beta_1X_{ij} + \beta_2X_{ij}T_{ij} $

And then comparing MI to MIII tests whether $\beta_2$ in MI is significantly different from 0.

However, I wouldn't compare models against each other this way. I would use AIC or BIC (I don't have a strong preference between them). Better yet, I'd use substantive knowledge to figure out which model is most sensible.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.