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Rich Mohn posted on Sunday, August 11, 2013  5:10 pm



Hello, the model below has random slopes and intercepts for the variable surgery . . . I'd like to correlate the intercepts and slopes for surgery. Any help would be appreciated. CLUSTER = clinic; WITHIN = base_qol surgery; ANALYSIS: TYPE = TWOLEVEL RANDOM; MODEL: %WITHIN% post_qol ON base_qol; s  post_qol ON surgery; 


You would say: %BETWEEN% post_qol WITH s; 

Rich Mohn posted on Monday, August 12, 2013  10:23 am



Thank you 


Hello! I am running a multilevel model with random intercepts and random slopes. The dependent variable is math achievement, the independent variable SES. The syntax is the following:  VARIABLE: NAMES = idc math ses; CLUSTER = idc; USEVARIABLES = math ses; WITHIN = ses; DEFINE: CENTER ses (GROUPMEAN); ANALYSIS: TYPE = twolevel random; MODEL: %WITHIN% slope  math ON ses; %BETWEEN% math WITH slope;  If I calculate the correlation between intercepts and slopes using the covariance of intercepts and slopes, the variance of the intercepts and the variance of the slopes (all in the regular Mplus output), my result is r = 0.214 If I save the values of the intercepts and slopes (using save=fscores) and then calculate the correlation between intercepts and slopes, my result is r = 0.357 What is the reason for the different values of the correlation? Which correlation should be used? Thank you in advance! 


Estimated factor scores don't behave quite like the true scores  see e.g. our FAQ Factor scores You should use the modelestimated correlation. 


Thank you for your answer! Allow me to raise one followup question. If I got your point right, your explanation refers to the latent modeling of intercept and slope used in Mplus. To check that I ran the same model in HLM and also saved the values of the intercepts and slopes and correlated them. The results are quite similar: the correlation within the model is r = 0.221, the correlation using the saved values is r = 0.376 Therefore, I assume that the difference between the two correlations is not due to the difference between true factor scores and estimated factor scores. Rather, I assume that the reason is connected with multilevel models in general. What do you think? 


I don't see how you reach your conclusion or what you mean by the difference being connected with multilevel models in general. The difference between modelestimated and factor score estimated correlations is well known in the literature as our FAQ points to. That's the whole story. 

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