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I fitted the following model to my data.

Linear regression model:
    NNSB ~ 1 + Gender + Age*MMRC

Estimated Coefficients:
                       Estimate     SE          tStat       pValue    
    (Intercept)           1.8004       1.027      1.7531      0.079978
    Age                 0.014051     0.01529     0.91898       0.35839
    Gender_Male          0.43134    0.099535      4.3335    1.6559e-05
    MMRC_MMRC 1         -0.64548      1.2465    -0.51785       0.60471
    MMRC_MMRC 2           2.5536      1.2689      2.0124      0.044513
    MMRC_MMRC 3           2.1066      1.3638      1.5447       0.12283
    MMRC_MMRC 4             2.07      1.5724      1.3164       0.18841
    Age:MMRC_MMRC 1     0.012023    0.018482     0.65052       0.51555
    Age:MMRC_MMRC 2    -0.034328    0.018843     -1.8218       0.06886
    Age:MMRC_MMRC 3    -0.026653    0.020307     -1.3125       0.18973
    Age:MMRC_MMRC 4    -0.016567    0.023175    -0.71488       0.47489

Could you help me in understanding the meaning of the last 4 coefficients? How should I read the ":" simbol?

MMRC is a categorical variable that can assume the values 0, 1, 2,3 and 4

gabboshow
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1 Answers1

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Matlab uses what I think is called Wilkinson notation for defining models. This is where the tilde (~) sign comes from too.

When you have a a*b term in your model, Matlab actually also includes any lower order terms. For example: y ~ a*b in Wilkinson notation actually corresponds to y = a + b + a*b in standard notation. If you just want a product in Wilkinson notation without any lower order terms (aka an 'interaction'), this is expressed as a:b. So, y ~ a*b is equivalent to y ~ a + b + a:b.

In your case, the first four MMRC terms correspond to the MMRC's on their own. The final four terms are the interactions between Age and MMRC.

RPM
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  • What you are saying is that my model is: NNSB ~ 1 + Gender + Age + MMRC + Age:MMRC? – gabboshow Aug 24 '15 at 09:50
  • should I take the interaction Age:MMRC as AgexMMRC? – gabboshow Aug 24 '15 at 09:52
  • Yes, your model corresponds to _NNSB ~ 1 + Gender + Age + MMRC + Age:MMRC_, and _Age:MMRC_ in Wilkinson notation corresponds to _Age x MMRC_ in 'standard' notation. – RPM Aug 24 '15 at 10:03
  • Thanks a lot. Since I have only 1 term with p < 0.05 (MMRC_MMRC 2) Can I assume that it is the only factor that affects the response variable? In particular, if a subject is MMRC2 he has +2 unit of NNSB with respect to a subject belonging to the other MMRC classes (assuming all the rest equal) – gabboshow Aug 24 '15 at 10:38
  • Gender has a p-value (much lower than) 0.05 – RPM Aug 24 '15 at 11:33
  • Yes! I didn't see it! So can I conclude that gender is the main factor that affect NNSB and then MMRC_MMRC2? – gabboshow Aug 24 '15 at 11:35
  • What the p-values are saying is that it is highly unlikely that gender has no influence on NNSB, and pretty unlikely that MMRC_MMRC2 has no influence on NNSB, but they do not say anything about how large an effect these variables have. The coefficient estimates indicate that MMRC_MMRC2 has a larger effect than gender, even when you take the standard errors into account. I should mention though that I am not a statistician and these conclusions should probably be accompanied by a plethora of caveats. – RPM Aug 24 '15 at 12:03
  • Say that the output is NNSB ~ 1 + Age*Gender + Age*MMRC, how would you convert it? Should I include the Age term twice? NNSB ~ 1 + Age + Gender + Age:Gender + Age + MMRC + Age:MMRC – gabboshow Aug 24 '15 at 23:53