Hello, my question is about the way to see the table of Covariance Analysis in JMP.
I have data above, and I consider Height as covariate, and I did Covariance Analysis.
First, I think the blue box is "adjusted mean" by covariate because actual mean for Control, Fast and Slow is 12.13, 9.41 and 15.83 respectively.
Therefore, second, the parameter estimate (Red box) provides intercept and τ1 and τ2 (τ3 =0), and then I can estimate that
Control : 9.6717502 - 0.142494 + 0.0558x
Fast: 9.6717502 - 3.286649 + 0.0558x
Slow: 9.6717502 + 0.0558x
The average of covariate (Height) is 49.9, and therefore, I can estimate that
Control : 9.53 + 0.0558 * 49.9 ≈ 12.314
Fast : 6.39 + 0.0558 * 49.9 ≈ 9.17
Slow : 9.6717502 + 0.0558 * 49.9 ≈ 12.457
Compared with adjusted mean in JMP (Blue box), Control and Fast is correct, but Slow is different. JMP says it's 15.885810.
My calculation for Slow is 12.457. Do I understand wrongly about Covariance Analysis, or JMP calculates in different ways unlike the general covariance analysis?
Could you let me know how I can interpret this?
Always many thanks!!!
You are close, but your models are a little off due to the way that JMP codes the categorical Fertilizer factor.
The easiest way to see what you want to see is to go to the red triangle and choose
Estimates > Show Prediction Expression:
or from the red triangle choose Estimates > Expanded Estimates:
The way that JMP does the coding requires that the estimates of a categorical variable add to 0. Thus, the estimate for slow = -1*(control estimate + fast estimate) = -1*(-.142494 + -3.286649) = 3.4291433, not 0.
Just some thoughts on your analysis. You should enter the covariate in the model first and use sequential tests to analysis the significance of the covariate. Also always check VIF's when using covariates. In your case they appear to be below 2 which is good.
Least square means are a function of the prediction formula set to some neutral value and is the mean of those nominal factor levels. I've added a data table with the fit model script and the resultant prediction formula saved. The LS means for Slow are indeed correct in JMP.
Thank you so much!! It's so clear!! I love "Prediction Expression" It looks like go good.
Many thanks.
