Continuous variable as independent variable and covariate

[#1]

Hi there,

I am trying to understand how do we define continuous variable as independent or covariate in JMP, in term of using them in fit model platform.

My current understanding is, unless one define design role as covariate to continuous variable, it is independent.  And, Model significance test, based on F-test, is called as ANOVA.

If continuous variable is defined as covariate, model significance test is called as ANCOVA.

Based on above understanding, I have fitted model using sample data "US Demographics" using least square platform for response "Eighth Grade Math" using "Region", "High School Graduates" and their interaction.

"High School Graduates" is considered as independent variable for mathematical purpose.

During first analysis, "High School Graduates" is used as is, without defining any design role (independent).

During 2nd analysis,  "High School Graduates" is defined as covariate in design role.

p-value for f-test and parameter estimate, estimate values and SS for model and error are same for first and second analysis. I am expecting some differences in model error terms, p-value for model and p-value of parameter estimates.

Is it that design role option in specific to DOE, if yes. How do I define continuous factor as independent or covariate for use in least square/Fit model.

Thanks!!

[#2 · Accepted solution]

You do not need to define anything. Simple cast the independent variable (data column) in Effects role after selecting Analyze > Fit Model. I assume that the data column is defined as Numeric data type and Continuous modeling type. You can verify the types by selecting the data column and then selecting Cols > Column Info.

The Design Role = Covariate is a column property usually created automatically when you design an experiment with JMP and add a covariate factor. The term 'covariate factor' in this case specifically refers to a variable that co-varies in time with the runs, its levels are pre-determined, and its effects are to be estimated in the model.

Why would you expect different results from the regression analysis?

[#3]

Thanks Mark!
With continuous variable included in an ANOVA, we have the analysis of covariance (ANCOVA).
Difference observed for shelf life prediction model SS (where time is covariate) and default ANOVA is due to Type of SS used. This is where i missed to hold.
Thank You!!

[#4 · Accepted solution]

The term covariate can be tricky to understand as its interpretation depends on how it is being used (context).  In a regression application where the data already exists, covariates are often just a continuous independent variable (and in ANCOVA, the other independent variables are likely categorical).  For DOE purposes, the covariate is typically an independent variable that is measured, but not specifically manipulated (often because the covariate is noise, a variable one is unwilling to control).  By accounting/assigning the covariate in the model, you increase the precision of detecting the design factor's effects.

For example, if you were running an experiment and you were concerned with ambient temperature effects.  You are unwilling to manage ambient temperatures, so you take the ambient temp. measurements during each run of the experiment.  When you write the model, you add the ambient temp. as a covariate (Typically put the covariate first in the model and use sequential tests (Type 1) for determining its significance.  The use partial tests (Type 3) for the remainder of the model effects.). This will account for the effects of ambient temperature (which otherwise would have been captured in the error term). By removing those effects from the error term (reduced MSE), you have increased the precision for testing the factors in the experiment.