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Help interpreting model with quadrati... |
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Hello, I am running an unconditional growth model of depression over time with 6 time points. I've run a linear model, and then tested to see if a model with a quadratic term fit better. The chi square difference was significant. However, I am confused about my results from the model with the quadratic term: 1) MY TLI is 1.009 2) The I-S covar is significant, the I-Q covar is significant, and the S-Q covar is significant... S WITH I -0.028 0.010 -2.649 0.008 Q WITH I 0.004 0.002 2.166 0.030 S -0.005 0.002 -2.794 0.005 3) However the means for the Slope and Quadratic are NOT SIGNIFICANT. Means I 0.592 0.011 53.939 0.000 S -0.006 0.009 -0.755 0.450 Q -0.002 0.002 -1.140 0.254 What would this mean? Is is still worth having the quadratic term in the model if the linear model overall fit is still very good? Thank you, Nicole |
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Note that if models differ with respect to a variance being free or fixed at zero, you cannot use a chi-square difference test to compare them but have to use BIC. I assume that your quadratic model has a free variance for the quadratic growth factor. A growth factor mean not being significant doesn't mean that the growth factor should be removed if it still has variance. |
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Dr. Muthen, The variance is significant: Variances I 0.109 0.015 7.295 0.000 S 0.029 0.009 3.217 0.001 Q 0.001 0.000 2.552 0.011 However, the BIC is slightly larger than that of the linear trajectory. I am sorry to ask but, I am confused as to why exactly I cannot use a chi-square difference test. Thank you for clarifying that for me. |
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BIC becomes larger for the quadratic model because of the insignificant q mean - you add a parameter which doesn't improve the likelihood much. Still, you would ignore the insignificance of the q mean, ignore the higher BIC, and keep the quadratic because it has variance. Likelihood-ratio chi-square difference testing is not ok when one of the models you are considering is a special case of the other by having parameter(s) on the border of their admissible space, such as a zero variance or a zero latent class probability. There is a large literature on that which you can google. |
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