I'm trying to figure out if I can use the ordinal logistic regression function with the data I have in order to create a set of prediction equations for estimating age-at-death. My response variables are ordinal (adolescent, young adult, middle adult, old adult), and my four predictor variables are continuous, but two are non-linear. I've tried transforming the predictor variables, but I can't seem to find a linear solution. If I've read correctly, the ordinal logistic regression analysis in JMP is based on a general linear model, so would that negate my being able to use the function due to my non-linear response variables (determined by the means of these variables when graphed by age category - i.e., the mean values rise to an asymptote in middle adulthood, then fall in value in old adulthood)? I've tried performing the analysis using the non-linear platform, but I receive an cautionary message because my Y variable is not continuous.
*Any* constructive advice is much appreciated! Also, on the most basic level, am I understanding the assumptions of the logistic model correctly?
In linear regression models, the response variable is continues.
In logistic regression models, the response variable is dichotomous. So we we choose appropriate link function ( probit,logit) to model it.
In all of the GLM models, the predictor variables can be continuous and discrete ( nominal, ordinal).
I don't understand (but two are non-linear):
"My response variables are ordinal (adolescent, young adult, middle adult, old adult), and my four predictor variables are continuous, but two are non-linear."
Your response variable is ordinal. So you can break it to 4 logistic regression:
You can also fit ordinal logistic regression, as you mentioned. Check this example in JMP website.
For more statistical details about these models , read "Introduction to categorical data analysis" or "categorical data analysis" by Alan Agresti , Wiley.
The assumptions for the independent variables isn't linearity ( and I don't even know what that would mean?)
A generalized linear models means the model is a linear combination, but the terms themselves can be quadratic. A non-linear model may have order statistics (max/min) and/or division/multiplication of terms that can't be expressed in a linear fashion.
y=x+ x^2 is still a GLM
y=cx/ax is a nonlinear model.