topic Re: How to do three-way Full Factorial ANOVA with unbalanced data with Mixed model? in Discussions

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

Juno — Thu, 05 Jan 2017 02:59:53 GMT

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!!

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

Mark_Bailey — Thu, 05 Jan 2017 12:34:55 GMT

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

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

That is all you cah do with this data.

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

txnelson — Thu, 05 Jan 2017 12:57:36 GMT

Mark,

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

Jim

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

Mark_Bailey — Thu, 05 Jan 2017 13:29:34 GMT

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?

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

Juno — Thu, 05 Jan 2017 13:33:30 GMT

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

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

Mark_Bailey — Thu, 05 Jan 2017 13:46:40 GMT

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).

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

Juno — Thu, 05 Jan 2017 15:32:25 GMT

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?

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

Mark_Bailey — Thu, 05 Jan 2017 16:14:15 GMT

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.

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

Mark_Bailey — Thu, 05 Jan 2017 16:19:09 GMT

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).

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

Juno — Thu, 05 Jan 2017 17:14:27 GMT

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!

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

Juno — Thu, 05 Jan 2017 17:47:24 GMT

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!

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

Mark_Bailey — Thu, 05 Jan 2017 18:34:03 GMT

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?

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

Juno — Thu, 05 Jan 2017 19:54:11 GMT

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

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

Mark_Bailey — Thu, 05 Jan 2017 20:11:07 GMT

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.

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

Juno — Thu, 05 Jan 2017 20:25:52 GMT

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

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

Mark_Bailey — Thu, 05 Jan 2017 20:35:09 GMT

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

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

Juno — Thu, 05 Jan 2017 21:23:27 GMT

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!

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

Mark_Bailey — Thu, 05 Jan 2017 21:39:48 GMT

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.

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

Juno — Thu, 05 Jan 2017 21:48:17 GMT

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.!

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

Mark_Bailey — Mon, 09 Jan 2017 15:41:00 GMT

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.