Great insights.

You need to explain at what level the variables are measured, I have no idea what valuation is. And school id Is not a random effect but a level 2 identifier. We need more information and more precision in the question.

The valuation is the final exam score of a student and it is measured at each student level. I want a predictive model that predicts these scores based on the given explanatory variables where I am thinking to consider school_id as a random effect.

Great insights.

Yes the mixed normal theory mixed (multilevel) model does seem appropriate. I presume that the entrance exam marks were prior to the valuation score. If you have both schools , current and past, you could fit a cross- classified model. You may also need a random coefficient model in which the slopes as well as intercepts are allowed to vary.

You are asking if a linear model is appropriate, as opposed, I assume to non-linear models (given that you capitalized Linear and not mixed, I assume you are aware that a multilevel model is appropriate, so your question is about linear v non-linear). Given "linear" can be include very curvy and discontinuous functions (e.g., interactions among piecewise polynomials), you probably can get the fit to be good, but that depends on your data and the fit of models. Without that information this seems difficult to answer.

Thank you Kelvyn Jones for your inputs.

Daniel Wright, Thank you for your input. I need suggestion if the linear mixed effect model is appropriate for this dataset. There is a non-linear relationship between the explanatory variable and the response variable. Also, I am considering school_id as my random effect or intercept. Also which is the best method to handle non-linearity in the model. Also please correct me if I am doing wrong in my modeling.

Priyanka Chudasama , there is an annoying meaning to phrases "linear model" and "linear regression" in statistics. They are annoying because they do not mean that the relationship between y and x is a straight line, so y_i = B0 + B1 x_i + B2 x_i^2 + e_i is not a straight line, but it is a linear regression because the Bs, which are estimated, are each multiplied by some function of the xs (which could be in separate columns, so let x_i^2 = z_i). So if the relationship is not a straight line this doesn't necessarily mean you need a non-linear regression. In some fields you have a specific model that would suggest you want a non-linear model, but I am assuming with test score data you probably do not. If necessary you might transform a variable (or use a generalized linear model). As far as the "best" approach to model non-straight lines, there is none. Depends on the situation and the data. General methods like cross-validation and fit indices can help.

So unless you have a reason, I'd probably avoid the non-linear route. On school_id being something, it is a level 2 identifier (and as Kelvyn Jones says, if students are in multiple schools there are more advanced options).

I think the mixed normal theory mixed model is seem appropriate.

I think your linear predictive.model.may be used

interesting

Try to work with regression models

The regression analysis modeol could do the job.

Thank you Priyanka Chudasama for your question. The multiple regression analysis can help as there are several variables and each variable should be considered.

I favorit google classroom, I think it more simply for Counting the mark and declare

This classic paper shows why mixed / multilevel models are potentially a major improvement over standard multiple regression for your problem

Using Empirical Bayes Techniques in the Law School Validity Studies

Donald B. Rubin Journal of the American Statistical Association Vol. 75, No. 372 (Dec., 1980), pp. 801-816

https://www.jstor.org/stable/2287165?seq=1

The reason fro the big improvement is that each school has relatively limited variation in the predictor variables but schools also do make a difference.

Kelvyn Jones Thank you for your answer and sharing the information