[R] Why are coefficient estimates using ML and REML are different in lme?

S Ellison S.Ellison at LGCGroup.com
Mon Oct 29 11:02:00 CET 2012

```Yi) Different criteria would be _exepcted_ to give different estimates.

ii) Look at teh standard errors on the coefficients. Essentially all of them are larger than the estimates for both fitting criteria.

Essentially, both models are telling you that your coefficients are not significantly different from zero.

S Ellison

________________________________________
From: r-help-bounces at r-project.org [r-help-bounces at r-project.org] On Behalf Of Houhou Li [lidarfly at yahoo.com]
Sent: 28 October 2012 23:55
To: r-help at r-project.org
Subject: [R] Why are coefficient estimates using ML and REML are different      in lme?

Hi, All,

My data collection is from 4 regions (a, b, c, d). Within each region, it has 2 or 3 units. Within each unit, it has measurement from about 25 sample site. I was trying to use lme function to discribe relationship between y and a few covariates. Both y and covariates were measured at the sample site level. My question is when I use exactlly the same model but choose different estimation method (ML vs REML), I got quite different coefficients esimate for fixed effect and variance estimate for random effect(see below). Can anyone here please help me to understand why? Thank you very much.

1) Using REML
lme(y~ Region*(x1+x2+x3), random=~1|unit, data=temp)

Linear mixed-effects model fit by REML
Data: temp
AIC      BIC    logLik
1498.871 1558.059 -731.4353
Random effects:
Formula: ~1 | unit
(Intercept) Residual
StdDev:    5.837025 7.104742
Fixed effects: y ~ Region * (x1 + x2 + x3)
Value Std.Error  DF   t-value p-value
(Intercept)                     162.28206 22.340090 193  7.264163  0.0000
Regionb                  -11.06624 24.582841   5 -0.450161  0.6714
Regionc                 5.01670 29.177730   5  0.171936  0.8702
Regiond                  -36.63434 26.262448   5 -1.394932  0.2218
x1                     0.04091  0.034732 193  1.177953  0.2403
x2                             -0.71649  0.356771 193 -2.008252  0.0460
x3                             -0.15945  0.375098 193 -0.425095  0.6712
Regionb:x1     -0.04451  0.046075 193 -0.965975  0.3353
.............

2) using ML
lme(y~ Region*(x1+x2+x3), random=~1|unit, data=temp, method="ML")
Linear mixed-effects model fit by maximum likelihood
Data: temp
AIC     BIC    logLik
1478.793 1539.38 -721.3964
Random effects:
Formula: ~1 | unit
(Intercept) Residual
StdDev: 0.0002763015 7.043271
Fixed effects: y ~ Region * (x1 + x2 + x3)
Value Std.Error  DF   t-value p-value
(Intercept)                     155.05508 21.512500 193  7.207674  0.0000
Regionb                   10.56095 21.981366   5  0.480450  0.6512
Regionc                 9.88513 28.595621   5  0.345687  0.7436
Regiond                  -34.68996 24.177548   5 -1.434801  0.2108
x1                     0.05274  0.033903 193  1.555701  0.1214
x2                             -0.67642  0.365633 193 -1.849995  0.0658
x3                              0.09977  0.293438 193  0.340007  0.7342
Regionb:x1     -0.05692  0.046042 193 -1.236259  0.2179

........

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