I have posted a similar message in the following link:

http://old.nabble.com/standard-error-for-the-estimated-value-(lmer-fitted-model)-td26414507.html

However, I did not get responses. I guess my question is not clear. Now, I

would like to clarify it and if someone is familiar with lmer modelling,

please give me a help. Thank you in advance for your attention!

Take a model fitted by lmer. The response is a binomial variable (proportion

or binary).

Now, the prediction based on fixed effects only can be calculated as

model at X%*%fixef(model).

According to an algorithm mentioned by Snedecor & Cochran (1989, p353), for

the normal response variable, the standard error for the estimated value

should be calculated as:

s*sqrt(vector(x)%*%inverse(t(model at X)%*%model at X)%*%t(vector(x))), where s is

the square root of the residual mean square, vector(x) is the vector at the

prediction point. For example, if the model has just one continuous

predictor, vector(x) should be (1,x) when the predictor value is x.

Then, how to calculate standard error for the estimated value in case of

binomial response data? In case of normal response variable, square root of

the residual mean square is easy to calculate. In case of binomial data, I

even don?t know how to calculate residual in logit scale, since in many

cases, logit(y) is immaterial when y is equal to 0 or 1, where y is

observations.

By the way, Douglas Bates once mentioned that it is possible to calculate

standard error for predictions based only on fixed effects. See the

following link:

http://tolstoy.newcastle.edu.au/R/e2/help/06/11/6180.html

?It is clear what the predictions based on the fixed effects only should be

and perhaps it is clear what the standard errors of those predictions are

(although that would be a case where my favorite topic of the degrees of

freedom associated with a standard error would rear its ugly head again).?

Does someone have any idea to solve the task mentioned by him? How about the

case of Poisson response variable?

Thank you very much!

Best regards,

Jianghua

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