Interpretation of effects

Eiko Fried <torvon at ...> writes:

Dear Mailinglist,

I might have to solve this problem in R. MPLUS support tell me they cannot
help me because the question is not MPLUS specific enough.

I'm a little confused.  Are you running the model in R or MPLUS?
If the former, could you please provide a reproducible example
( e.g. see http://tinyurl.com/reproducible-000 )?  If the latter,
I don't quite understand why the question is "not MPLUS specific enough"
(maybe they consider it a general statistical question, and that the
MPLUS documentation should be sufficient to indicate how MPLUS
parameterizes models?  I don't know ...)

I am not sure where to inquire about this, maybe you guys can help me out.

I'm running something that is basically a mixed effects model in MPLUS,
which is set up as growth model. I allow every person to have its own
intercept and slope.

5 measurement points, 1 ordered dependent variable (0-3), quadratic growth
term has better fit, so I use a quadratic slope.

I am predicting intercept and slope by two covariates, one is a centered
metric (intelligence), the other nominal (gender).

Results:
Intercept: gender is significant (negative estimate -0.6)
Slope: gender is significant (positive estimate 0.2)

So in lme your model would be

  lme(response ~ (intelligence+gender)*poly(time,2), 
     random=(poly(time,2)|individual),
    data=... )  

?

(Maybe?  I'm not quite sure I've specified the predictor by time
interaction correctly ... and I'm not sure whether you're just trying
to use a pure quadratic model, and if so whether you can justify
a pure quadratic [i.e. setting the linear term to zero] ... however,
all of that is separate from any mixed-model issues yo

I want to plot this covariate now, over time (male vs female), and am not
sure how to do this.

(1) Coding is 1=female, 0=male. Do I understand correctly that this means
that males are higher at baseline (higher by 0.6 points on the dependent
variable, I guess?), and that females rise higher in the slope? Do they
rise by 0.2 per measurement point on the dependent variable, or 0.2 over
all 5 measurement points, or something entirely different?

That sounds right; the female slope per unit of the continuous
predictor should be 0.2 greater than the male slope.  (But I don't
know exactly what you mean by 'quadratic slope' above -- I'm now
guessing you mean pure quadratic.)

(2) How can I find out whether the two trajectories meet (males start
higher, females rise quicker ...)? That is, do females overtake males at
some point, or are maler going to be higher throughout?

I think you'd need to do a bit of algebra on this.

(3) If the effects were not on gender, but on a centered, metric variable,
like intelligence - what exactly would -0.6 and 0.2 mean?

It would mean the slope with respect to time increased or decreased
by the relevant amount per unit of intelligence.

  None of these questions are specific to mixed models, they all 
have to do with the coding of parameters in linear models more
generally.  I don't know where this is covered best: maybe see
one of Crawley's books, or Faraway's books on linear models.  Perhaps
others have suggestions.

  Ben Bolker