In a repeated measures design, how are the degrees of freedom calculated?
Namely, how is the value 114 calculated in the lme output?
#Using lme
baseline <- lme(attitude ~ 1, random = ~1|participant/drink/imagery, data = longAttitude, method = "ML")
drinkModel <- update(baseline, .~. + drink)
imageryModel <- update(drinkModel, .~. + imagery)
attitudeModel <- update(imageryModel, .~. + drink:imagery)
anova(baseline, drinkModel, imageryModel, attitudeModel)
#> Model df AIC BIC logLik Test L.Ratio
#> baseline 1 5 1503.590 1519.555 -746.7950
#> drinkModel 2 7 1498.461 1520.812 -742.2306 1 vs 2 9.12891
#> imageryModel 3 9 1350.529 1379.265 -666.2644 2 vs 3 151.93237
#> attitudeModel 4 13 1316.512 1358.020 -645.2560 3 vs 4 42.01676
#> p-value
#> baseline
#> drinkModel 0.0104
#> imageryModel <.0001
#> attitudeModel <.0001
attitudeModel <- lme(attitude ~ drink*imagery, random = ~1|participant/drink/imagery, data = longAttitude)
summary(attitudeModel)
#> Linear mixed-effects model fit by REML
#> Data: longAttitude
#> AIC BIC logLik
#> 1309.22 1350.062 -641.6101
#>
#> Random effects:
#> Formula: ~1 | participant
#> (Intercept)
#> StdDev: 0.0007071812
#>
#> Formula: ~1 | drink %in% participant
#> (Intercept)
#> StdDev: 6.201306
#>
#> Formula: ~1 | imagery %in% drink %in% participant
#> (Intercept) Residual
#> StdDev: 7.404812 0.2787554
#>
#> Fixed effects: attitude ~ drink * imagery
#> Value Std.Error DF
#> (Intercept) 7.894444 0.9726183 114
#> drinkAlcoholvsWater 2.188889 0.6877450 38
#> drinkBeervsWine -1.750000 1.1912092 38
#> imageryNegativevsOther 6.738889 0.3905443 114
#> imageryPositivevsNeutral -6.633333 0.6764426 114
#> drinkAlcoholvsWater:imageryNegativevsOther 0.190278 0.2761565 114
#> drinkBeervsWine:imageryNegativevsOther 3.237500 0.4783171 114
#> drinkAlcoholvsWater:imageryPositivevsNeutral 0.445833 0.4783171 114
#> drinkBeervsWine:imageryPositivevsNeutral -0.662500 0.8284696 114
#> t-value p-value
#> (Intercept) 8.116694 0.0000
#> drinkAlcoholvsWater 3.182704 0.0029
#> drinkBeervsWine -1.469095 0.1500
#> imageryNegativevsOther 17.255121 0.0000
#> imageryPositivevsNeutral -9.806203 0.0000
#> drinkAlcoholvsWater:imageryNegativevsOther 0.689021 0.4922
#> drinkBeervsWine:imageryNegativevsOther 6.768522 0.0000
#> drinkAlcoholvsWater:imageryPositivevsNeutral 0.932087 0.3533
#> drinkBeervsWine:imageryPositivevsNeutral -0.799667 0.4256
#> Correlation:
#> (Intr) drnkAW drnkBW imgrNO
#> drinkAlcoholvsWater 0
#> drinkBeervsWine 0 0
#> imageryNegativevsOther 0 0 0
#> imageryPositivevsNeutral 0 0 0 0
#> drinkAlcoholvsWater:imageryNegativevsOther 0 0 0 0
#> drinkBeervsWine:imageryNegativevsOther 0 0 0 0
#> drinkAlcoholvsWater:imageryPositivevsNeutral 0 0 0 0
#> drinkBeervsWine:imageryPositivevsNeutral 0 0 0 0
#> imgrPN dAW:NO dBW:NO dAW:PN
#> drinkAlcoholvsWater
#> drinkBeervsWine
#> imageryNegativevsOther
#> imageryPositivevsNeutral
#> drinkAlcoholvsWater:imageryNegativevsOther 0
#> drinkBeervsWine:imageryNegativevsOther 0 0
#> drinkAlcoholvsWater:imageryPositivevsNeutral 0 0 0
#> drinkBeervsWine:imageryPositivevsNeutral 0 0 0 0
#>
#> Standardized Within-Group Residuals:
#> Min Q1 Med Q3 Max
#> -0.0819512018 -0.0196920226 0.0007259018 0.0237264898 0.0979229869
#>
#> Number of Observations: 180
#> Number of Groups:
#> participant drink %in% participant
#> 20 60
#> imagery %in% drink %in% participant
#> 180
Created on 2018-07-21 by the reprex package (v0.2.0).