> library(nlme)
> out.r <- lme(Y ~ SG + VP + V10 + EP, random = ~ 1 | No)
> summary(out.r)
Linear mixed-effects model fit by REML
 Data: NULL
       AIC      BIC    logLik
  166.3820 175.4528 -76.19098

Random effects:
 Formula: ~1 | No
        (Intercept) Residual
StdDev:    1.445028 1.872146

Fixed effects: Y ~ SG + VP + V10 + EP
                Value Std.Error DF   t-value p-value
(Intercept) -6.134690 14.555917 21 -0.421457  0.6777
SG           0.219397  0.146956  6  1.492947  0.1861
VP           0.545861  0.520588  6  1.048547  0.3348
V10         -0.154244  0.039967  6 -3.859288  0.0084
EP           0.157177  0.005588 21 28.128410  <.0001
 Correlation:
    (Intr) SG     VP     V10
SG  -0.694
VP  -0.715  0.067
V10 -0.934  0.433  0.836
EP   0.011  0.023 -0.116 -0.197

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max
-1.7807117 -0.6063671 -0.1069013  0.4571818  1.7811918

Number of Observations: 32
Number of Groups: 10
>  out.little <- lm(Y ~ SG + VP + V10 + EP)
> anova(out.r, out.little)
           Model df      AIC      BIC    logLik   Test  L.Ratio p-value
out.r          1  7 166.3819 175.4528 -76.19098
out.little     2  6 167.7402 175.5152 -77.87011 1 vs 2 3.358266  0.0669
> 1 - pchisq(2 * 3.358266, 1)
[1] 0.00955232
> 1 - pchisq(3.358266, 1)
[1] 0.06686844
> #### But this is one-tailed test, so
> (1 - pchisq(3.358266, 1)) / 2
[1] 0.03343422
>

> # So we accept H1 and keep the random effects!!!!!

> out.r2 <- lme(Y ~ EP, random = ~ 1 | No)
> summary(out.r2)
Linear mixed-effects model fit by REML
 Data: NULL
       AIC      BIC   logLik
  183.4306 189.0354 -87.7153

Random effects:
 Formula: ~1 | No
        (Intercept) Residual
StdDev:    8.387862  1.88046

Fixed effects: Y ~ EP
                Value Std.Error DF   t-value p-value
(Intercept) -33.30626  3.287182 21 -10.13216  <.0001
EP            0.15757  0.005703 21  27.62679  <.0001
 Correlation:
   (Intr)
EP -0.582

Standardized Within-Group Residuals:
       Min         Q1        Med         Q3        Max
-1.6759908 -0.4857902 -0.0397993  0.5128182  1.8518206

Number of Observations: 32
Number of Groups: 10
> out <- lm(Y ~ No + EP - 1)
> anova(out.r2, out)
       Model df      AIC      BIC    logLik   Test  L.Ratio p-value
out.r2     1  4 183.4306 189.0354 -87.71530
out        2 12 133.1165 145.6508 -54.55825 1 vs 2 66.31409  <.0001
Warning message:
Fitted objects with different fixed effects. REML comparisons are not meaningful. in: anova.lme(out.r2, out)
> out.r2d2 <- lme(Y ~ EP, random = ~ 1 | No, method = "ML")
>  anova(out.r2d2, out)
         Model df      AIC      BIC    logLik   Test  L.Ratio p-value
out.r2d2     1  4 178.6625 184.5255 -85.33126
out          2 12 141.6956 159.2845 -58.84781 1 vs 2 52.96689  <.0001
> # nonnested comparison so not clear what this means
> # classical likelihood theory invalid
>