Hello Mr Witold, 

Are you doing moderation test on gender and ?

I think it is comparable to adding time-invariant covariates in HLMs to predict random slopes and/or random intercepts. 

If you center age before adding as predictor, the mean of the intercept in the MPlus output would represent the expected initial level of your modeled variable for a person with average age in respect to your sample and with a gender coded with 0.

If the path is significant, it indicates that the expected intial level of your modeled variable increases by 0.176 units if age increases by one unit for a person which gender is coded with 0.  

Does this make sense to you?

BEST

@ Manuel, I think I understood most of your explanation. Thank you. 

However, the path for gender was non-significant. So why does this significant estimate of 0.176 pertain to sex coded as 0?

Also, is it age increasing by one unit or the modeled variable (alcohol use measured across 3 time points)?

Thanks for clarifying.

Witold

First, it is age increase by one unit, then the expected value for alcohol use at T1 increase by .176 units.

Why taking gender into account?:

Because gender is a part of your model, and therefore should be taken into account when interpreting the results.

EV(intercept) = mean(intercept) + b1*X1(Gender) + b2*X2(age)

assume that X1 is non-significant and b = .05 and X2 is significant and b2 = .176. In addition, gender is coded 0=female and 1 = male. 

than the expected intercept for a women with a mean age (if age was centered) would be calculated as followed (X1=0 and X2=0 since age was centered):

EV(intercept) = mean(intercept) + 0*.05(Gender) + .176*0(age)

EV(intercept) = mean(intercept)

However, the expected intercept for a men with a mean age (if age was centered) would be calculated as followed (X1=1 and X2=0 since age was centered):

EV(intercept) = mean(intercept) + 1*.05(Gender) + .176*0(age)

EV(intercept) = mean(intercept) + 1*.05.

and if age increase one unit, it would look like this for men:

EV(intercept) = mean(intercept) + 1*.05(Gender) + .176*1(age)

EV(intercept) = mean(intercept) + 1*.05. + 1*.176

However, you might remove gender after finding it was not significant. 

Hope that helps,

Best