Hi,
I'm playing around with gamlss and don't entirely understand the sigma
result from an attempted lognormal fit.
In the example below, I've created lognormal data with mu=10 and sigma=2.
When I try a gamlss fit, I get an estimated mu=9.947 and sigma=0.69
The mu estimate seems in the ballpark, but sigma is very low. I get similar
results on repeated trials and with Normal and standard normal
distributions. How should I understand sigma in these results?
cheers,
RdR
######### Example #########
# enable reproduction
set.seed(1234)
# create some lognormal data
X <- rlnorm(1000,meanlog=10,sdlog=2)
# try gamlss fit
gLNO <- gamlss(X~1,family=LNO)
summary(gLNO)
*******************************************************************
Family: c("LNO", "Box-Cox")
Call: gamlss(formula = X ~ 1, family = LNO)
Fitting method: RS()
-------------------------------------------------------------------
Mu link function: identity
Mu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.947 0.06305 157.8 0
-------------------------------------------------------------------
Sigma link function: log
Sigma Coefficients:
Estimate Std. Error t value
(Intercept) 0.69 0.02236 30.86
Pr(>|t|)
(Intercept) 2.19e-147
-------------------------------------------------------------------
No. of observations in the fit: 1000
Degrees of Freedom for the fit: 2
Residual Deg. of Freedom: 998
at cycle: 2
Global Deviance: 24111.45
AIC: 24115.45
SBC: 24125.27
*******************************************************************
Warning message:
In summary.gamlss(gLNO) :
summary: vcov has failed, option qr is used instead
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