gls() vs. lme() in the nlme package

Question

In the nlme package there are two functions for fitting linear models (lme and gls).

1. What are the differences between them in terms of the types of models that can be fit, and the fitting process?
2. What is the design rational for having two functions to fit linear mixed models where most other systems (e.g. SAS SPSS) only have one?

Update: Added bounty. Interested to know differences in the fitting process, and the rational.

Answer 1

From Pinheiro & Bates 2000, Section 5.4, p250:

The gls function is used to fit the extended linear model, using either maximum likelihood, or restricted maximum likelihood. It can be veiwed as an lme function without the argument random.

For further details, it would be instructive to compare the lme analysis of the orthodont dataset (starting on p147 of the same book) with the gls analysis (starting on p250). To begin, compare

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orth.lme <- lme(distance ~ Sex * I(age-11), data=Orthodont) summary(orth.lme)  Linear mixed-effects model fit by REML  Data: Orthodont         AIC     BIC    logLik   458.9891 498.655 -214.4945  Random effects:  Formula: ~Sex * I(age - 11) | Subject  Structure: General positive-definite                       StdDev    Corr                 (Intercept)           1.7178454 (Intr) SexFml I(-11) SexFemale             1.6956351 -0.307               I(age - 11)           0.2937695 -0.009 -0.146        SexFemale:I(age - 11) 0.3160597  0.168  0.290 -0.964 Residual              1.2551778                       Fixed effects: distance ~ Sex * I(age - 11)                            Value Std.Error DF  t-value p-value (Intercept)           24.968750 0.4572240 79 54.60945  0.0000 SexFemale             -2.321023 0.7823126 25 -2.96687  0.0065 I(age - 11)            0.784375 0.1015733 79  7.72226  0.0000 SexFemale:I(age - 11) -0.304830 0.1346293 79 -2.26421  0.0263  Correlation:                        (Intr) SexFml I(-11) SexFemale             -0.584               I(age - 11)           -0.006  0.004        SexFemale:I(age - 11)  0.005  0.144 -0.754  Standardized Within-Group Residuals:         Min          Q1         Med          Q3         Max  -2.96534486 -0.38609670  0.03647795  0.43142668  3.99155835   Number of Observations: 108 Number of Groups: 27 

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orth.gls <- gls(distance ~ Sex * I(age-11), data=Orthodont) summary(orth.gls)  Generalized least squares fit by REML   Model: distance ~ Sex * I(age - 11)    Data: Orthodont         AIC      BIC    logLik   493.5591 506.7811 -241.7796  Coefficients:                           Value Std.Error  t-value p-value (Intercept)           24.968750 0.2821186 88.50444  0.0000 SexFemale             -2.321023 0.4419949 -5.25124  0.0000 I(age - 11)            0.784375 0.1261673  6.21694  0.0000 SexFemale:I(age - 11) -0.304830 0.1976661 -1.54214  0.1261   Correlation:                        (Intr) SexFml I(-11) SexFemale             -0.638               I(age - 11)            0.000  0.000        SexFemale:I(age - 11)  0.000  0.000 -0.638  Standardized residuals:         Min          Q1         Med          Q3         Max  -2.48814895 -0.58569115 -0.07451734  0.58924709  2.32476465   Residual standard error: 2.256949  Degrees of freedom: 108 total; 104 residual 

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Notice that the estimates of the fixed effects are the same (to 6 decimal places), but the standard errors are different, as is the correlation matrix.