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Repeated vs Replicates vs multiple observations and nesting

Bhavya

Hi JMP community,

I have been working on a biological data set where I need help in which model should I use to analyze my data. There are 2 different strains of mice (2 mice per strain) and 1 leg of each mouse has been given treatment 1, the other leg of the same mouse has been given treatment 2. I have taken 2-5 measurements during my experiment (chemical composition) per leg of each mouse. I am interested in using mixed model to compare means of chemical composition between each strain within a treatment and between treatment within a strain of mouse. Here is an example JMP table date set.

I don't particularly want to average the multiple observations, for the sake of making use of the in-sample variability in my stats. Thus, looking for a method where I can compare means, without losing the information that I get from making multiple observations, but also don't want to consider each observation as an independent observations or sample.

I use this particular table, and go to fit model> mixed model> then have mineral amount as a y variable, fixed effect as strain, treatment condition, strain* treatment condition, random effect as mouse number. I don't do any nesting and repeated measures. Should I be considering any?

Thank you for your help!

JMP help.jmp

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Mark_Bailey

What is the nature of the repeated measurements? Why did you measure the chemical more than once? Are the measurements taken close in time? Are the measurements taken over a period of time? Is time recorded so that it might be modeled and tested as another fixed effect?

Your model makes sense and using the individual measures makes sense, depending on how you answer these questions.

Bhavya

What is the nature of the repeated measurements? Why did you measure the chemical more than once? - measurement has been taken more than once, since it's a microscale imaging technique, which is very sensitive to sample surface roughness of the bone (extracted after sacrificing the mice). To avoid errors arising from the in sample variation, I did multiple measures, so I have a distribution of values to compare between samples.

Are the measurements taken close in time? Are the measurements taken over a period of time? Is time recorded so that it might be modeled and tested as another fixed effect? - All of the multiple measurements are not time sensitive, they are only 1 minute apart (the amount of time it takes the instrument to take a single measurement and move to next point on the sample surface, which is less than 10 microns away).

I guess, the two biggest concerns I have are that:
1) If I do mixed model, how do I make sure that the model is not considering every single measurement as a single independent sample?
2) How to I make sure that I am accounting for the fact that measures for treatment 1 and treatment 2 are coming from the same mouse?

Thank you!

Mark_Bailey

Thank you for answering my questions!

The mixed model that you propose only assumes that every observation is sampling the same random error. It represents variation from sacrificing the mouse, harvesting the leg, and so on all the way to measurement error. That is to say, the errors are poolable into a single variance component. Your model is a statement that you do not expect the population of errors to vary mice. Another way to say it is that you are sampling the same population of errors regardless of which mouse.
Well, mouse number acts like a blocking factor with a random effect so your proposed model should be correct. Additionally, the factor levels in your factor data columns should indicate the shared conditions. You factors are crossed, not nested. That is to day, Strain 1 is always Strain 1. Strain 1 is not something different in each mouse or treatment. Similarly, Treatment 1 is always the same treatment regardless of which mouse strain. Factors that are truly nested can be analyzed with JMP by indicating the specific nesting for each term in the model. Your measurements are blocked by mouse number.

statman

Only adding to what Mark has already said and given guidance on. The multiple measures taken in a short period of time are indeed nested and are a potentially good estimate of measurement error. I would first look at those measures. Do they make sense? A simple plot of the data will help. How much variation is there? Is the variation consistent? Are there any unusual measurements? Is an average a good estimate of those measures? (averaging will reduce the measurement error)