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 · Accepted solution]

You can fit a model with all of the desired effects except for the Year*Location interaction effect.

1. Select Analyze > Fit Model.
2. Select the Year, Location, and Variety data columns.
3. Click Macros and select Factorial to Degree.
4. Select the Year*Location effect and click Remove.
5. Select the Year and the Year*Variety terms, then click the red triangle next to Attributes and select Random.
6. Click Run.

That is all you cah do with this data.

[#3]

Mark,

You are not qualifying anything about the Year*Location*Variety term.  That term will remain viable in this design? 

Jim

[#4]

I did not consider the three-factor interaction effect. Two of the three two-factor interaction effects may be estimated if the only missing values are for Location = B when Year = 2012. To be sure, I made a full factorial design for these factors as they were described and had not trouble estimating the parameters if the Year*Location term was omitted.

Who believes in three-factor interactions anyway?

[#5]

Hello Mark,

Thank you very much for your answer. I assume I would have to remove the Year*Location*variety term from the model as well?

Will I still be able to see the effect from year on the yield then? Thank you

Juno

[#6]

The estimability of parameters depends on the design the 32-run full factorial design (2*2*8) supports estimation of all possible terms, assuming that all are treated as nominal factors. The missing data prohibits the estimation of the Year*Location effect and the Year*Location*Variety effect.

Further, if you treat Year as a random effect, then you won't want to estimate the Year*Variety effect. You can estimate the Year effect regardless of how you model it (fixed or random effect).

[#7]

Hello Mark,

Thank you so much! 

Will I still be able to get the LSD for all the varieties from this combined analysis so I can make pairwise comparisons? 

[#8]

You will need to use the Fit Least Squares platform through Analysis > Fit Model. Make sure that the Emphasis is Effect Leverage, although there is another way to get this information. The Least Squares Means are reported below each of the Leverage Plots. The LSD is not available but you can test all the pairwise differences with the Tukey method, differences with a control level with Dunnett's method, or any specific contrast or combination of contrasts. Click the red triangle next to any one of the Leverage Plots to find the commands. If you press and hold the Ctrl (Windows) or Command (Mac) first, the command will be broadcast to all of the Leverage Plots so you don't have to do each one individually.

[#9]

I forgot that you are fitting a mixed model. My nstructions suited the case of a model with only fixed effects.

These commands are still available but they are located elsewhere. Open the Effect Details outline and you will find the same information for each term as you would in the Leverage Plot (except for the plot itself).

[#10]

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!