a) What can be an appropriate method to fit this kind of model? I had referred so much literature where description about iterative generalized least squares, multi-level model, separate regression model, weighted least-square model are given. But still I am not getting how to use and fit estimated value of parameters in interaction term and get separate coefficients for both interaction parameter?

a) What can be an appropriate method to fit this kind of model? I had referred so much literature where description about iterative generalized least squares, multi-level model, separate regression model, weighted least-square model are given. But still I am not getting how to use and fit estimated value of parameters in interaction terms and get separate coefficients for both interaction parameters?

I am having difficulty in fitting model on data. Basically, I have data about the evaluation of phenotypic property(i.e. hard) of 65 palm trees by 5 judges. As an evaluation scheme, each judge provides score to each sample. For 3 judges sample data look like this:

Judge Product Hard

aa 1 5

ab 1 6

ac 1 3

aa 1 7

ab 1 5

ac 1 4

aa 2 5

ab 2 8

ac 2 6

aa 2 7

ab 2 4

ac 2 4

Yij = αi + βiθj + εij i=judge, j=product

Here, αi is judge main coefficients, βi is judge coefficients due to difference in their scoring pattern and θj is product coefficients and εi is assessor dependent.

I was trying to fit this model using lme function in R, but difficulty I am facing to fit the interaction term because model here fitted for parameters rather than co-variates.

My queries here is:

a) Can you suggest me what can be an appropriate method to fit this kind of model. I had refer so many literature where description about iterative generalized least square, multi-level model, separate regression model, weighted least-square model are given. But still I am not getting how to use and fit estimated value of parameter in interaction term and get separate coefficients for both interaction parameter?

c) which R package can I used?

Regards

I am having difficulty in fitting a model on data. Basically, I have data about the evaluation of phenotypic property  (i.e. hard) of 65 palm trees by 5 judges. As an evaluation scheme, each judge provides score to each sample. For 3 judges sample data look like this:

Judge       Product                  Hard

aa             1                      5

ab             1                      6

ac             1                      3

aa             1                      7 

ab             1                      5

ac             1                      4

aa             2                      5

ab             2                      8

ac             2                      6

aa             2                      7
 
ab             2                      4

ac             2                      4 

$$Y_{ij} = α_i + β_iθ_j + ε_{ij}$$ i = judge, j = product

Here, $α_i$ is judge main coefficients, $_i$ is judge coefficients due to difference in their scoring pattern and $θ_j$ is product coefficients and $ε_i$ is assessor dependent.

I was trying to fit this model using lme function in R, but difficulty I am facing to fit the interaction term because model here fitted for parameters rather than co-variates.

My queries here are:

a) What can be an appropriate method to fit this kind of model? I had referred so much literature where description about iterative generalized least squares, multi-level model, separate regression model, weighted least-square model are given. But still I am not getting how to use and fit estimated value of parameters in interaction term and get separate coefficients for both interaction parameter?

c) which R package can I use?