I have a repeated measurement data of adherence to a treatment over 7 months of study period. I hypotetize that the adherence will fluctuate from every month. What is the appropriate analysis to test if there is significant fluctuation or not?
I fyou want to test for a trend (are the values changing significantly over time) there are several methods. The easiest way is certainly to fit a linear model and look if the slope of the regression line is significantly different from 0 (means p-value in your software
My study refers to your second answer. I would like to see the ups and downs of the adherence from one month to another. If I apply the general linear model I don't think I can see the monthly fluctuation.
I found one test, chi square of trend, if you ever heard of it. But I am still not sure of it as well.
fit a sinus model to the series to estimate the amplitude, phase, frequency, and possibly other parameters relevant to your model (e.g. damping rate). The confidence interval for the amplitude can be obtained by bootstrapping.
Another approach you could take is via a latent growth modeling. It is designed to uncover trends in data. The basic/traditional approach is to hypothesis your growth as linear, or some form of polynomial. However, more useful to your case would be to set the first two times on the slope to 0 and 1, then freely estimate the rest. If you are unfamiliar with this approach, a very good read on the subject can be found in:
Little, T. D. (2013). Longitudinal structural equation modeling: New York : The Guilford Press.
The latent growth modeling will be totally new for me so thank you for the refference, Tim!
I just tried to use one-way repeated ANOVA, though it might not give me the exact analysis of the trend but rather the difference of one data point compared to others. Unfortunately my data is very not normally distrubuted and I could not log transform them as there are 0 cases in the data. Then I tried to use non parametric Friedman test and will proceed with Benferroni test in case of significant result.
Ugh. Missing data and non-normality. The bane of statistics.
If you are willing to take a leap, you might consider Structural Equation Modeling (SEM) which can be used for observed variables (and latent growth modeling). A program like Mplus can handle missing data (it uses FIML) and is able to quite nicely handle non-normality (e.g., using a MLR estimator as one approach).
Is there any appropriate statistical test to compare which trend model( ex: linear, quadratic, parametric etc.) performs better for time series data of export of ready made garments?
Note: I used regression analysis technique to fit those models separately.
Analysis of variance, if the models are nested (like polynomial of different degrees [linear, quadratic,...]). If the models are not nested, I don't know how to formally test (I don't even know if you couldformulate a meaningful statistical hypothesis that would be testable), but you could compare the AICs.