Dear Hamed

Structural equation models will be useful approach for your research purpose, you can use Path Analysis which extract direct and indirect contributions between several variables and also the effect of errors so provide you t values and their significancy for the path coefficients. It's available by using LISREL which is easy to analyze with.

Rana

Thank you for the comment dear Rana.

Dear Haghi,

You can SPSS for any data value but You must be comparison predicted data with reel data. For this purpose, You can make statistical analysis. For example RMSE (root mean square error) or VAF variant analysis frequency. If you want to calculation table for RMSE and VAF.

Dr. Umucu

Hamed -

As I think Rana indicated, there may be substantial interactions between these variables. It is not a matter of assigning a given percent of influence to each regressor, as far as I know, because the influence assignable to a given regressor may be strongly modified by each different combination of other regressors you may use. These can be very tangled relationships. Also, when you include nonlinearity and crossterms, it is difficult to know what do you want to consider. Do you want to know the influence of x3, or ln(x3), or x3x5, in relation to what other such variables or terms?

Depending upon what you want to know, you might look at various situations. A good start in analyzing your data may be to look at a variety of scatterplots comparing variables or terms such as above, just two at a time.

Perhaps you would like to rank the relative importance of regressors, when they are considered independently? You could look at the estimated variance of the prediction error, and compare these estimates for some predicted y values using (1) the full model you theorized, and (2) one regressor at a time.

That might give you a start at analyzing your model, and learning more about your data. But remember that in statistics you can find data correlations, but not causality. You have to rely on subject matter theory, and see if data support your theory. Generally it is best to make your model as simple as possible, to avoid just modeling noise.

In addition, noise can make sorting out complex relations such as noted above, impossible.

FYI, for prediction (not forecasting), for continuous data, one place you can find software to produce the square root of the estimated variance of the prediction error for individual y predictions for some experiments would be STDI in SAS PROC REG. I suppose R and other software may have something like that as well.

It seems that you might be interested in the relative importance of your regressors, and you could look at them one at a time in simple linear regressions as noted above, but also as indicated, this will not tell you about multicollinearity or other various interactions.

I think it important to emphasize the potential usefulness of starting with a good look at a variety of scatterplots.

As for PCA, I think that will take you a bit further from understanding the relative influence of various regressors, but someone more knowledgable about that and other aspects of your question may have better thoughts on that.

I hope at least some of this was related to your question. :-)

Cheers - Jim

Thanks all for your comments; I will read them in details and will come back to you accordingly.

The classical way for assessing the contribution of explanatory variables in regression analysis is the analysis of variance. Each variable "accounts for" a certain amount of the total variance of the response variable, and so their relative contributions can be quantified. However, this technology works best in designed experiments in which the effects of each explanatory are orthogonal. With observational data, or data from non-orthogonal experiments, there are many different possibilities for the amount of variance that can be associated with a given variable. It depends on the order in which variables are fitted, so you get, for example, the amount of variance accounted for by X3, after adjusting for the effects of X1 and X2, and ignoring the effects of X4 and X5. It sounds complicated, and it is, because in the absence of orthogonality, no analysis can uniquely attribute variance between explanatory variables that are more or less confounded or correlated. A common approach is to look at the effect of each explanatory variable after adjusting for all the others (though beware of fitting nonsense models if some of your effects are interactions), perhaps backed up with the effect of each ignoring the effects of all the others. SAS refers to sums of squares based on these approaches as Type II and Type I, respectively.

Dear colleagues;

Please check the attached Excel worksheet; it is ANOVA Table for 2 responses (Grade and Recovery). There are 3 variables including interactions and  curvature effect. I have prepared ANOVA table and just want to calculate pure contribution percent ignoring Residual and Errors. The models are significant. Please check attached file and let me know your comments about best way for calculation of Pure Contribution Percent of each factor in model.

Thank you in advance for your valuable comments in advance.

Best regards,

Hamed

To calculate the contribution percentage, you can simply divide the F-value of each contributing parameter to the sum of F-values.

Could you please answer,

How could I get the percent contribution in case of simple linear regression e,g Just two variables (x= litterfall and Y= c/n ratio, therefore what is the contribution of litter to explain c/n ratio variation from the correlation.)

Respect to a non-linear regression approach, you can use random forest (RF) and variables importance. If you have a high-dimensional dataset, you can use a wrapper of RF using the BORUTA approach (see: https://www.jstatsoft.org/article/view/v036i11/v36i11.pdf)

Thanks for your comments Fabian.