I want to know about the Nonlinear Mixed Effect Model.
This is my conducted analysis below.
1. Construct base model.
2. Scatterplot between estimated parameters and covariates.
3. Integrate high correlated covariates to the base model.
4. Construct covariate model.
For example, estimates is k, and covariates is x.
ln(k) and x are positively correlated.
And I defined that k=theta1*theta2^(x-Med(x)).
Med(x) means median of x.
Objective function value of constructed covariate model is significantly less than that of base model.
However, in covariate model, estimated theta2 is less than 1.
Why? I cannot understand it.
↓This is my thought.
k=theta1*theta2^(x-Med(x)).
ln(k)=ln(theta1)+(x-Med(x))*ln(theta2)
ln(k)=ln(theta2)*x+ln(theta1)-Med(x)*ln(theta2)
That theta2 is less than 1 means that ln(theta2) is less than 0.
So, ln(k) and x are negatively correlated.
It is contradictory with regression results.
I am unfamiliar to this area.
If you have some information, please teach me.
Contradictory thoughts may occur in a situation you are not able to take a proper decision on a matter. It is good as it shows your thinking process is still going on. It is a part of human thoughts that it creates contradictory points to get the best out of what you are thinking.
Quick question, is (x-med(x)) roughly symmetric? A negative value here determines the impact of theta2. If there is a tendency to skew then this may be part of it. There may be a constant in k that ought to be accounted for. Easier to understand the estimation when we understand something about the data as well.
Good luck,
Thanks, Oddson
I already checked skewness of the covariate.
This was negative value (-0.226), but I think this covariate means near to normal distribution.
In addition, k's skewness was 2.22 (far from normal distribution).
Is this a problem? I do not know the relation between this value and the contradiction.
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