How to do three-way Full Factorial ANOVA with unbalanced data with Mixed model?

[#1]

Hello ,

I am trying to do the yield data analysis with three factors (2 yeras, 2 locations, 8 varieties). However the data is not a balanced data as following: 

In 2012,  the 8 varieties were tested only in location A, but in 2013, the 8 varieties were tested in locations A and B.

How do I still run a full-factorial 3-way anaysis using Mixed Model if I want to treat "year" as random effect?  because I wtill wish to see if there are any interactions between the three factors. 

Thank you very much for your help!! 

[#2]

Hello Mark,

Thank you very much for explaing it so clear. 

I understand that if I run the Mixed Model with "year" as random effect, I won't be able to obtain a common LSD, but still can do pairwise comparisons.  

However, will I be able to get a LSD if I run it by "Year" ?

Y : Yield

By Year

Model Effcts: Varieties, Locations, Varieties*Locations

Thank you!

[#3]

I do not see a need to perform separate analyses for each year. This division of the sample will affect the power of your tests. Keep all the effects in the model that are supported by the data for the most powerful tests. You will get a whole model test, tests for individual terms, and tests to compare levels within a factor.

Why won't the commands I gave you earlier be sufficient for the comparisons that you want to make?

[#4]

Because 2012 has less rainfall than 2013, and not all of the varities are responding to the year the same. I can combine, but I will need to check for the CV% for each enviornment combination before doing the combining analysis. 

Do you know how to check for the CV% for each combination to make sure they are low enough to combine? 

ex (2012, location A) & (2012, location B) & ((2013, location A)& (2013, location B)

Thank you

[#5]

So you will remove Year from the analysis?

Rainfall is just one of presumably many perturbations that contribute to the random effect labelled as Year. Would it make sense to switch from a random categorical factor (Year) to a fixed continuous factors like rainfall?

Variety is a fixed effect that depends on the level of another factor? That effect requires an interaction term in the model.

If you have multiple crops in your data set and you combine them, then the additional variation across years or crops will reduce the power of your tests.

Because you are comparing the same response across all of the groups, you don't need to use %CV. You can compare the variance directly in the Oneway platform. Select Analyze > Fit Y by X. Click the red triangle after you launch the platform and select Unequal Variances. The Bartlett's test is the most powerful test for normally distributed data. The Levene's test is the most powerful test otherwise.

You can also use the Normal Quantile Plot command in Oneway to assess normality of the data.

[#6]

No,  I still need the Year in my model to see if most of the varieties perform stably across different enviornments. Your point of rainfall is the only variable in a year makse a lot of sense. However I thought there is a way to look at the Year* variety interactions even though the year is random? 

CV is a common way for to look at the uniformity of the fields when conducting yield trial with any experimental design, such as RCBD. 

It's generally belived that < 10% is extremely uniform enviornments ;

10%< x <30% is acceptable before further combining analysis

[#7]

You can use the Tabulate platform (Analyze menu) to compute the %CV for each group in a summary format.

[#8]

Thank you so much for all your help! 

I am going to analyze Disease rating as well (ordinal data) , will you please suggest me a best model to analyze given my situation ? (8 varieties, 2 years, and 2 locations)? 

Appreciate it again!

[#9]

The model terms will be the same but the method will be nominal or ordinal logistic regression. JMP cannot estimate such a model if there are random effects. You might be better off treating Year as a fixed effect for now, as you only have two years, which is a very small sample size for estimating the variance anyway.

Start as before with Fit Model. JMP will automatically switch to nominal logistic regression when you put your categorical response Disease in the Y role. (Don't enter another response in this case.) The difference between nominal and ordinal logistic is the interpretation of the logit and the odds that you want.

[#10]

I didn't know Year can be treated as fixed effect for any situation, but thank you for this reccomnedation. 

If I fit Ordinal Logistic model, I get to see if the effects or interactions are siginificantly different, right?  Is there a way I can maye pairwise comparison between the varieties for their Disease response ratings? 

Thank you.!

[#11]

You will have tests for individual terms in the model.

There are no pair-wise tests (e.g., Tukey or contrasts) in Ordinal or Nominal Logistic.The parameter estimates report will test all parameters agains the last level but without adjustment for the multiple comparisons.