R: nlme: can we use varIdent or varFixed to model known variances?

Question

Can anyone familiar with nlme kindly explain how does the varIdent, with option fixed actually work?

Documentation says:

fixed....an optional numeric vector, or list of numeric values, specifying the values at which some or all of the coefficients in the variance function should be fixed.

What is coefficient in variance function to be fixed? Is it something like variance=kx, where k is the coefficient and x predictor, or variance itself is to be fixed (then it would be strange to use 'coefficient of variance function', unless variance function would be something like varCov=kI, where I is identity matrix).

What I really want to do is to fit a model, where variance is pre-set, a priori known for each value of outcome and was wondering if I can use varIdent for this purpose.

EDIT: after consulting some literature I understand now that varIdent models variance as var=k*var1, where var1 is variance of reference level of given predictor and option 'fixed' allows to pre-specify the values of the coefficient.

Now I would like to know if I can use varIdent also to model a priori known, exact values of variances associated with observations of continous outcome at different values of continous predictor, that is, use it to incorporate measurment error in the model.

For example, I have measurments Yobs with SDs ysd, what about model:

gls(Y~X, weights=varIdent(ysd), data=data) ?

Can anyone help?

Answer 1

If you have actual variances for each observation and wish to use these in your nlme model, you can indeed specify these directly using the weights argument in the gls function.

To fit a model with actual variances in nlme, try the following approach:

gls(Y ~ X, weights = varWeights(1/variances), data = data)

In this model:

Y is your outcome variable. X is your predictor(s). variances is a vector containing the actual variances for each observation. varWeights is used to specify the known variances as weights, which should be the inverse of the variances since gls uses precision weights (the inverse of the variance). By specifying 1/variances, you are incorporating the actual measurement error into the model, and each observation will contribute to the fitting process inversely proportional to its variance.

varIdent with the fixed option in nlme is used to specify fixed variances for different levels of a categorical factor, scaling the variances by an estimated proportionality constant. It's useful when variances differ across groups but are consistent within them. varFixed, on the other hand, assumes that the variance structure is known and constant across all observations, scaled by a single proportionality constant. It applies when you have a uniform variance adjustment factor for the entire dataset. Essentially, varIdent allows for group-specific variance scaling, while varFixed applies a global scaling factor.