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| Model of cubic growth term failed to ... |
 
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| Anh Hua posted on Saturday, May 16, 2020 - 5:33 pm
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I'm running a longitudinal analysis with ~300 students whose reading performance is tracked over 3 years. My goal is to find a functional form (linear, quadratic, and cubic, etc) that best describes the association between students’ instruction time and students’ reading achievement. The instruction time variable ranges from 0 to 28 months.
I've run 4 analyses: (1) unconditional means model (2) model with fixed and random linear effects of time (3) unconditional quadratic growth model, which includes fixed and random effects of months and months^2; and (4) unconditional cubic growth model which includes the fixed and random effects of linear, quadratic, and cubic growth terms.
For the quadratic model, the results show that the variance of the quadratic growth term is 0.000, standard error is 0.000, and it is statistically significant. Question 1: How should I interpret this finding and is it worth including the random quadratic effect in my model?
For model #4, I encountered this: “ One or more variables have a variance greater than the maximum allowed of 1000000.
Check your data and format statement or rescale the variable(s) using the DEFINE command.”
The variance greater than 1,000,000 is not a typo. So question #2: How do I rescale my time variables in such a way that helps the model to converge but is also methodologically meaningful? |
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| As a first step, use Define to scale your variables to have variances between 1 and 10 (e.g. divide a variable by 10). |
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| Anh Hua posted on Sunday, May 24, 2020 - 6:13 pm
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Dear Dr. Muthen,
Thank you so much for your suggestions. I have some clarification/follow up questions for you:
Q1. To confirm my understanding, I should rescale ALL the variables included in my model, which are my time variables AND reading scores, i.e., my DV, is this correct? I guess this because I did it both ways (rescaling only my time variables and rescaling all) and the ratio of parameter estimates to standard errors remain identical in the latter case.
Q2. If that's true, how does the transformation change the interpretation of my grand mean? So in particular, the DV reading score previously ranged from 124 to 239, now they go from 12.4 to 23.9. The grand mean for the quadratic growth model used to be 191 and now, it is 19.1, which is an out of range value.
Q3. My model with the cubic growth term shows that the variance of cubic growth curves is not statistically significant, although the graph that I plotted that show individual growth curves shows (to the naked eye) that there’s a lot of variability. How can this be so? Perhaps it just means that the variability that I observe may not be best captured by the variability of the cubic growth function (but rather by the quadratic growth curve function as the variance of the quadratic growth term is significant). Is my interpretation correct?
Thank you so much for all your help. |
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Q1. You want to get the variances of your DVs to be in the range of approx 1 - 10. The time variable should not be re-scaled in this way.
Q2. You interpret results in the new scale.
Q3. We need to see your full output to say - send to Support along with your license number. |
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| Anh Hua posted on Tuesday, May 26, 2020 - 5:10 pm
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Dear Dr. Muthen,
Thank you for your prompt response.
Regarding your point for Q1: Okay, I see that I need to transform my DV by dividing it by a constant to get the variance in between 1-10, but how should I rescale my time variables as the cubed time variable seems to be the culprit that led to model non-convergence? My original time variable was coded in months of instruction, and across the 3 years, the values ranged from 0 months to 28 months. When these time variables were cubed, the variance increased to 46,354,447. Therefore, Q1a: In addition to rescaling my DV by dividing it by 10, how should I rescale my time variables? Q1b. Is there a reference that I can use to justify my decision to transform my variables this way to the readers?
Please see my second question in the next post. |
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| Anh Hua posted on Tuesday, May 26, 2020 - 5:21 pm
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I wonder if the reason that my cubic growth model did not converge is that my models are too restrictive. I had posted my non-convergence problem on SEMNET https://listserv.ua.edu/cgi-bin/wa?A2=ind1912&L=SEMNET&P=R32906&X=10DFAEE6CDCDC1002C&Y=myautumn28%40yahoo.com and someone suggested that I try GAMM. I then studied the literature on GAMM and applied it to my analyses only to realize that the results did not make sense. I then followed up with my questions here (https://listserv.ua.edu/cgi-bin/wa?A2=ind2001&L=SEMNET&P=R20328&X=10DFAEE6CDCDC1002C&Y=myautumn28%40yahoo.com) and here https://stats.stackexchange.com/questions/445399/how-to-interpret-the-smoothed-effect-of-time-in-gamm-models and I was not able to get an answer.
I'd greatly appreciate your advice if you think there’s a better methodology given my research questions and data.
Thank you and I will send you my output shortly. |
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| Anh Hua posted on Monday, June 22, 2020 - 6:33 am
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Good morning, Dr. Muthen,
I've tried to rescale by time variables by dividing them by 10 (as time cubed has variance way greater than 1000000), as recommended by you, and the models ran. However, I'm reticent to transform these variables because I would like to interpret the results in the original scale, and not in the new scale with the transformed variables.
Is there another way to get my models to converge without having to transform my time variables? Thank you so much for any advice you can provide. I've been stuck with this problem for so long and not sure what else to do. |
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| Once you have gotten the converged model estimates, you can re-scale your estimates back to the original scale. I won't go through and tell you how - we don't do statistical consulting - but you can check that you do it right by seeing that you get estimated reading means in the original scale. |
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| Anh Hua posted on Tuesday, June 23, 2020 - 7:47 am
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Dear Dr. Muthen,
Thank you so much for taking the time and giving me the hint. I will start searching for ways to rescale my estimates so that I can interpret the results in their original scale. I will also explore other methodologies too (e.g. piecewise growth modeling, etc).
Thank you again. Your advice always teaches me something new! |
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