Hi Fellows,
In a longitudinal research, 30 (for example) preschoolers were assessed roughly biweekly over a year on a cognitive task called, say, "Bright Brain". A participant could use one of three strategies in an assessment: "C", "B", "A", in order of level of development. (Consider Siegler's overlapping waves model.) The question is how the use of strategies develops. Specifically, do children show stronger preference for the more advanced strategies over time?
As aforementioned, the dependent variable is categorical with three levels. I plan to do a logistic regression with age (months) as a continuous predictor. But a problem is that children (inevitably) missed some assessments. None of them attended all 20 assessments, and several were frequently absent and were observed for just 11 or 12 times. So I wonder if such a high rate of missing data would threaten the analysis, or if there is a better way of modeling.
ANOVA is not preferred. While it is technically possible to calculate the proportion of each strategy a children used in each of the four seasons (quarters), and see if the mean proportion of a strategy differed across time (seasons) and if there was a dominating strategy overall and in a given season, there were too few assessments in a season to ensure precise calculation of proportion.
Let me know if any information necessary for your judgment is missing.
Best
Meng
You need a method that handles the missing data without dropping cases. If this is just in the outcomes (you have complete data on covariates) then a multilevel logistic regression could be OK. You have a lot of missing data but if there is autocorrelation between sessions then it might not be as impactful as you think (as 11 or 12 sessions might be OK).
If you have missing data on covariates (e.g., time varying covariates) then you need some way to impute the missing information. This could be done with full information maximum likelihood in MPLUS or via multiple imputation (e.g., using an R package such as brms).
'30 (for example) preschoolers were assessed roughly biweekly over a year on a cognitive task (dependent variable) and age (months) as a continuous predictor'. Multinomial logistic regression is best method to analyse this type of data. But out of maximum of 20 assessments several were frequently absent (and were observed for just 11 or 12 times). In this scenario it is better to repeat the study with improvement in obtaining measurement from all participants for each assessment, because whatever analysis (simulation, imputation...) you do will be misleading. Off course for academic purpose you can try these methods.
Thank you all for promising suggestions. The study was conducted several years ago, and it is unlikely in the foreseeable future that we can collect additional data, so I'll try to make the best out of the current data.
Dr. Yarnold, what do you mean by "uniformly" and "consistently"?
Dr Paul my intention is not to say (generally) simulation research will be misleading. Rather, with so much of missing information (several were observed for just 11 or 12 times out of 20 times, the number of persons completing all 20 assessment will be few out of 30 participants) it is possible that simulation research will be misleading. More explicitly, unless the reasons for such high non-response is clear, definitely it will be misleading.
I have but another point. Is this a case of unbalanced observations or missing observations? Participants were assessed for different numbers of times (from 11 to 19), but when a participant did attend an assessment, everything (date, outcome, any covariate) was properly recorded.
This is probably way too simple, but: Could you do something like a complexity score. Strategy C earns 1 point, B earns 2, and A earns 3. So a student solves a problem 20%C, 40%B, and 60%A for a total of 0.2+0.8+1.8=2.8. Now run a simple regression predicting the score based on hours of instruction. This corrects for students that miss instructional hours regardless of whether they missed any one exam.
It is more problematic if missing an exam is equivalent to missing instructional hours, or taking an exam happens even if the student did not get the class time. In this case one might guess that students that miss class will start to perform badly, and this path will become worse unless some intervention by students/teachers/parents is made to enable the student to catch up to the rest of the class.