I'm sorry if this has been asked before. I searched the archives but couldn't find a similar question although it looks like a simple one.
I am fitting a mixed effect regression model. Consider that this is my full model:
m1 = lmer(y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8+ x9 + x10 + (1 | Subject), data = df)
And the output of this full model is as follows. Note that I used lmerTest
packacage for the calculation of p values:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -1.712e-02 1.433e-01 1.920e+03 -0.119 0.90491
x1 -2.376e-02 8.999e-03 7.910e+02 -2.640 0.00845 **
x2 2.524e-02 1.243e-02 3.544e+02 2.031 0.04297 *
x3 5.638e-03 8.853e-03 2.182e+03 0.637 0.52428
x4 9.676e-03 1.387e-02 2.182e+03 0.698 0.48553
x5 9.014e-03 6.298e-03 2.082e+03 1.431 0.15255
x6 -3.017e-02 1.717e-02 2.199e+03 -1.757 0.07906
x7 -5.920e-03 5.524e-03 2.189e+03 -1.072 0.28397
x8 1.082e-02 9.891e-03 2.191e+03 1.094 0.27396
x9 2.736e-02 1.680e-02 2.052e+03 1.629 0.10342
x10 1.239e-02 1.257e-02 2.174e+03 0.986 0.32432
Therefore, both x1 and x2 seem to be the significant effects. But then I dropped x1 and x2 respectively to build two reduced models.
m2 = lmer(y ~ x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + (1 | Subject), data = df)
m3 = lmer(y ~ x1 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + (1 | Subject), data = df)
I compared these reduced models against the full model using ANOVA. Only x1 improved the model, not x2.
anova(m1, m2)
Models:
..1: y ~ x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + (1 | Subject)
object: y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + (1 | Subject)
Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
..1 12 901.57 970.16 -438.79 877.57
object 13 896.06 970.37 -435.03 870.06 7.5068 1 0.006146 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
anova(m1, m3)
Models:
..1: y ~ x1 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + (1 | Subject)
object: y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + (1 | Subject)
Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
..1 11 896.54 959.42 -437.27 874.54
object 13 896.06 970.37 -435.03 870.06 4.4747 2 0.1067
This is the output of the first reduced model, that is m2, without x1:
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -6.403e-02 1.424e-01 2.228e+03 -0.450 0.6529
x2 1.313e-02 8.458e-03 2.210e+03 1.552 0.1207
x3 1.488e-02 1.374e-02 2.209e+03 1.083 0.2789
x4 1.147e-02 6.187e-03 2.215e+03 1.854 0.0639
x5 -1.920e-02 1.673e-02 2.206e+03 -1.148 0.2512
x6 -4.886e-03 5.544e-03 2.237e+03 -0.881 0.3782
x7 -6.745e-03 7.405e-03 2.215e+03 -0.911 0.3625
x8 2.394e-02 1.668e-02 2.210e+03 1.435 0.1515
x9 1.243e-02 1.260e-02 2.221e+03 0.987 0.3237
x10 1.917e-02 1.196e-02 2.207e+03 1.602 0.1092
And this is the output of the second reduced model, that is m3, without x2:
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 9.813e-02 9.574e-02 2.241e+03 1.025 0.30549
x1 -2.156e-02 8.098e-03 2.215e+03 -2.662 0.00781 **
x3 1.072e-02 1.385e-02 2.209e+03 0.773 0.43936
x4 6.864e-03 6.218e-03 2.215e+03 1.104 0.26980
x5 -2.797e-02 1.696e-02 2.208e+03 -1.649 0.09937
x6 -6.422e-03 5.526e-03 2.238e+03 -1.162 0.24529
x7 6.368e-03 9.610e-03 2.218e+03 0.663 0.50761
x8 3.044e-02 1.527e-02 2.206e+03 1.994 0.04632 *
x9 7.137e-03 1.218e-02 2.223e+03 0.586 0.55813
How is it possible? Is it because x2 has a relatively low t (and therefore, high p) value? And under these circumstances, is x2 a significant predictor or not?
Thank you.
Update: Upon the request of @Tahir, I added ANOVA results and outputs of two reduced models.