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I've noticed a discrepancy in the SEs of the fixed effect estimates given by the nlme::lme function. Specifically, the SEs in the summary output differ from the square root of the diagonal entries of the estimated variance-covariance matrix . Here is an example:

library(nlme) fit=lme(Yield~Time+Variety,Alfalfa,random=~1|Block,method="ML")

The summary output gives the following SEs:

> summary(fit) ... Fixed effects: Yield ~ Variety Value Std.Error DF t-value p-value (Intercept) 1.5716667 0.11013218 64 14.270731 0.0000 VarietyLadak 0.0945833 0.07947391 64 1.190118 0.2384 VarietyRanger -0.0191667 0.07947391 64 -0.241169 0.8102 ...

The estimated variance-covariance matrix gives somewhat different values:

> sqrt(diag(fit$varFix)) (Intercept) VarietyLadak VarietyRanger 0.10781334 0.07780059 0.07780059

Any insight would be much appreciated!

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The documentation in help("summary.lme") answers your question:

adjustSigma

an optional logical value. If TRUE and the estimation method used to obtain object was maximum likelihood, the residual standard error is multiplied by $\sqrt{n_{obs}/(n_{obs} - n_{par})}$, converting it to a REML-like estimate. This argument is only used when a single fitted object is passed to the function. Default is TRUE.

This adjustment is also applied to the parameters' standard errors. If you set adjustSigma = FALSE you get the expected result.

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  • $\begingroup$ Thank you so much! That works. $\endgroup$ Commented Jun 23, 2023 at 5:55

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