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Errors-in-variables multivariate polynomial regression (R)

(EDIT: the question has been modified just a little bit to be more specific)

I want to fit a multivariate polynomial regression that accounts for measurement errors (an Error-in-Variables model).

As an example, my input data is like:

y      sd_y      x       sd_x       z       sd_z

9.55   0.26     6.74     0.71      0.25     0.02
8.31   0.19     5.93     0.33      -0.40    0.05
...    ...      ...      ...        ...     ...   

where sd_y, sd_x, sd_z are the standard deviations of each variable, and

 wx <- 1/(sd_x)**2 ; wy <- 1/(sd_y)**2 ; wz <- 1/(sd_z)**2 

would be the weights for each variable.

If I use a standard regression model (where predictors are supposed to have been measured exactly or without error) my function or fit, in R, would be:

p <- lm(y~polym(x, z, degree = 2, raw=TRUE))

Is there a method/package in R that allows to deal with “error-in-variables models”? If so, how I would write my fit p when using the supposed package?


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