This function computes the null-model (i.e. (y ~ 1)) of
a model. For mixed models, the null-model takes random effects into account.
Examples
data(sleepstudy)
m <- lmer(Reaction ~ Days + (1 + Days | Subject), data = sleepstudy)
summary(m)
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ Days + (1 + Days | Subject)
#> Data: sleepstudy
#>
#> REML criterion at convergence: 1743.6
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -3.9536 -0.4634 0.0231 0.4634 5.1793
#>
#> Random effects:
#> Groups Name Variance Std.Dev. Corr
#> Subject (Intercept) 612.10 24.741
#> Days 35.07 5.922 0.07
#> Residual 654.94 25.592
#> Number of obs: 180, groups: Subject, 18
#>
#> Fixed effects:
#> Estimate Std. Error t value
#> (Intercept) 251.405 6.825 36.838
#> Days 10.467 1.546 6.771
#>
#> Correlation of Fixed Effects:
#> (Intr)
#> Days -0.138
summary(null_model(m))
#> Linear mixed model fit by REML ['lmerMod']
#> Formula: Reaction ~ (1 + Days | Subject)
#> Data: structure(list(Reaction = c(249.56, 258.7047, 250.8006, 321.4398,
#> 356.8519, 414.6901, 382.2038, 290.1486, 430.5853, 466.3535, 222.7339,
#> 205.2658, 202.9778, 204.707, 207.7161, 215.9618, 213.6303, 217.7272,
#> 224.2957, 237.3142, 199.0539, 194.3322, 234.32, 232.8416, 229.3074,
#> 220.4579, 235.4208, 255.7511, 261.0125, 247.5153, 321.5426, 300.4002,
#> 283.8565, 285.133, 285.7973, 297.5855, 280.2396, 318.2613, 305.3495,
#> 354.0487, 287.6079, 285, 301.8206, 320.1153, 316.2773, 293.3187,
#> 290.075, 334.8177, 293.7469, 371.5811, 234.8606, 242.8118, 272.9613,
#> 309.7688, 317.4629, 309.9976, 454.1619, 346.8311, 330.3003, 253.8644,
#> 283.8424, 289.555, 276.7693, 299.8097, 297.171, 338.1665, 332.0265,
#> 348.8399, 333.36, 362.0428, 265.4731, 276.2012, 243.3647, 254.6723,
#> 279.0244, 284.1912, 305.5248, 331.5229, 335.7469, 377.299, 241.6083,
#> 273.9472, 254.4907, 270.8021, 251.4519, 254.6362, 245.4523, 235.311,
#> 235.7541, 237.2466, 312.3666, 313.8058, 291.6112, 346.1222, 365.7324,
#> 391.8385, 404.2601, 416.6923, 455.8643, 458.9167, 236.1032, 230.3167,
#> 238.9256, 254.922, 250.7103, 269.7744, 281.5648, 308.102, 336.2806,
#> 351.6451, 256.2968, 243.4543, 256.2046, 255.5271, 268.9165, 329.7247,
#> 379.4445, 362.9184, 394.4872, 389.0527, 250.5265, 300.0576, 269.8939,
#> 280.5891, 271.8274, 304.6336, 287.7466, 266.5955, 321.5418, 347.5655,
#> 221.6771, 298.1939, 326.8785, 346.8555, 348.7402, 352.8287, 354.4266,
#> 360.4326, 375.6406, 388.5417, 271.9235, 268.4369, 257.2424, 277.6566,
#> 314.8222, 317.2135, 298.1353, 348.1229, 340.28, 366.5131, 225.264,
#> 234.5235, 238.9008, 240.473, 267.5373, 344.1937, 281.1481, 347.5855,
#> 365.163, 372.2288, 269.8804, 272.4428, 277.8989, 281.7895, 279.1705,
#> 284.512, 259.2658, 304.6306, 350.7807, 369.4692, 269.4117, 273.474,
#> 297.5968, 310.6316, 287.1726, 329.6076, 334.4818, 343.2199, 369.1417,
#> 364.1236), Days = c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3,
#> 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4,
#> 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5,
#> 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6,
#> 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7,
#> 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8,
#> 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
#> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0,
#> 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9), Subject = structure(c(1L,
#> 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
#> 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L,
#> 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
#> 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L,
#> 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L,
#> 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 10L,
#> 10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L,
#> 11L, 11L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 13L,
#> 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 14L, 14L, 14L, 14L,
#> 14L, 14L, 14L, 14L, 14L, 14L, 15L, 15L, 15L, 15L, 15L, 15L, 15L,
#> 15L, 15L, 15L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L,
#> 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 17L, 18L, 18L, 18L,
#> 18L, 18L, 18L, 18L, 18L, 18L, 18L), levels = c("308", "309",
#> "310", "330", "331", "332", "333", "334", "335", "337", "349",
#> "350", "351", "352", "369", "370", "371", "372"), class = "factor")), row.names = c(NA,
#> 180L), class = "data.frame")
#>
#> REML criterion at convergence: 1769.8
#>
#> Scaled residuals:
#> Min 1Q Median 3Q Max
#> -4.0449 -0.4486 0.0089 0.4819 5.2186
#>
#> Random effects:
#> Groups Name Variance Std.Dev. Corr
#> Subject (Intercept) 651.6 25.53
#> Days 142.2 11.93 -0.18
#> Residual 654.9 25.59
#> Number of obs: 180, groups: Subject, 18
#>
#> Fixed effects:
#> Estimate Std. Error t value
#> (Intercept) 257.76 6.76 38.13