检查线性混合效应模型的正态性假设

Checking the normality assumption of a linear mixed effects model

我有以下 LME 代码:

IDRTlme <- lme(Score ~ Group*Condition, random = ~1|ID, data=IDRT)

我想检查正态性假设,所以我完成了以下测试:

shapiro.test(resid(IDRTlme))

这是对 lme 的输出进行 Shapiro 测试的正确方法吗?如果不是,那么非常感谢任何帮助?

如有任何帮助,将不胜感激!

IDRT 数据如下:

structure(list(ID = c("1993", "1993", "1993", "1993", "1993", 
"1993", "1997", "1997", "1997", "1997", "1997", "1997", "19998", 
"19998", "19998", "19998", "19998", "19998", "3122", "3122", 
"3122", "3122", "3122", "3122", "3152", "3152", "3152", "3152", 
"3152", "3152", "3182", "3182", "3182", "3182", "3182", "3182", 
"330", "330", "330", "330", "330", "330", "354", "354", "354", 
"354", "354", "354", "363", "363", "363", "363", "363", "363", 
"369", "369", "369", "369", "369", "369", "370", "370", "370", 
"370", "370", "370", "375", "375", "375", "375", "375", "375", 
"377", "377", "377", "377", "377", "377", "378", "378", "378", 
"378", "378", "378", "379", "379", "379", "379", "379", "379", 
"380", "380", "380", "380", "380", "380", "381", "381", "381", 
"381", "381", "381", "3862", "3862", "3862", "3862", "3862", 
"3862", "3872", "3872", "3872", "3872", "3872", "3872", "388", 
"388", "388", "388", "388", "388", "390", "390", "390", "390", 
"390", "390", "392", "392", "392", "392", "392", "392", "393", 
"393", "393", "393", "393", "393", "394", "394", "394", "394", 
"394", "394", "395", "395", "395", "395", "395", "395", "396", 
"396", "396", "396", "396", "396", "399", "399", "399", "399", 
"399", "399", "5512", "5512", "5512", "5512", "5512", "5512", 
"382", "382", "382", "382", "382", "382", "1001", "1001", "1001", 
"1001", "1001", "1001", "1002", "1002", "1002", "1002", "1002", 
"1002", "1003", "1003", "1003", "1003", "1003", "1003", "1004", 
"1004", "1004", "1004", "1004", "1004", "1005", "1005", "1005", 
"1005", "1005", "1005", "1006", "1006", "1006", "1006", "1006", 
"1006", "1007", "1007", "1007", "1007", "1007", "1007", "1008", 
"1008", "1008", "1008", "1008", "1008", "1009", "1009", "1009", 
"1009", "1009", "1009", "1012", "1012", "1012", "1012", "1012", 
"1012", "1013", "1013", "1013", "1013", "1013", "1013", "1014", 
"1014", "1014", "1014", "1014", "1014", "1015", "1015", "1015", 
"1015", "1015", "1015", "1016", "1016", "1016", "1016", "1016", 
"1016", "1017", "1017", "1017", "1017", "1017", "1017", "1020", 
"1020", "1020", "1020", "1020", "1020", "1021", "1021", "1021", 
"1021", "1021", "1021", "1024", "1024", "1024", "1024", "1024", 
"1024", "1025", "1025", "1025", "1025", "1025", "1025", "1026", 
"1026", "1026", "1026", "1026", "1026", "1027", "1027", "1027", 
"1027", "1027", "1027", "1088", "1088", "1088", "1088", "1088", 
"1088", "1192", "1192", "1192", "1192", "1192", "1192", "1422", 
"1422", "1422", "1422", "1422", "1422", "1492", "1492", "1492", 
"1492", "1492", "1492", "1592", "1592", "1592", "1592", "1592", 
"1592", "1602", "1602", "1602", "1602", "1602", "1602", "1642", 
"1642", "1642", "1642", "1642", "1642", "171", "171", "171", 
"171", "171", "171", "1722", "1722", "1722", "1722", "1722", 
"1722", "1732", "1732", "1732", "1732", "1732", "1732", "174", 
"174", "174", "174", "174", "174", "175", "175", "175", "175", 
"175", "175", "1752", "1752", "1752", "1752", "1752", "1752", 
"1762", "1762", "1762", "1762", "1762", "1762", "1782", "1782", 
"1782", "1782", "1782", "1782", "1802", "1802", "1802", "1802", 
"1802", "1802", "182", "182", "182", "182", "182", "182", "184", 
"184", "184", "184", "184", "184", "1852", "1852", "1852", "1852", 
"1852", "1852", "186", "186", "186", "186", "186", "186", "187", 
"187", "187", "187", "187", "187", "188", "188", "188", "188", 
"188", "188", "1892", "1892", "1892", "1892", "1892", "1892", 
"190", "190", "190", "190", "190", "190", "192", "192", "192", 
"192", "192", "192", "1924", "1924", "1924", "1924", "1924", 
"1924", "193", "193", "193", "193", "193", "193", "195", "195", 
"195", "195", "195", "195", "196", "196", "196", "196", "196", 
"196", "197", "197", "197", "197", "197", "197", "1982", "1982", 
"1982", "1982", "1982", "1982", "1992", "1992", "1992", "1992", 
"1992", "1992", "19922", "19922", "19922", "19922", "19922", 
"19922", "1999", "1999", "1999", "1999", "1999", "1999", "19992", 
"19992", "19992", "19992", "19992", "19992", "199924", "199924", 
"199924", "199924", "199924", "199924", "199945", "199945", "199945", 
"199945", "199945", "199945", "199949", "199949", "199949", "199949", 
"199949", "199949", "199951", "199951", "199951", "199951", "199951", 
"199951", "199952", "199952", "199952", "199952", "199952", "199952", 
"199j2", "199j2", "199j2", "199j2", "199j2", "199j2", "490", 
"490", "490", "490", "490", "490", "181", "181", "181", "181", 
"181", "181", "3812", "3812", "3812", "3812", "3812", "3812", 
"199950", "199950", "199950", "199950", "199950", "199950", "191", 
"191", "191", "191", "191", "191"), Condition = structure(c(1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 
2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 
6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 
4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L, 1L, 2L, 3L, 4L, 5L, 6L), .Label = c("neutral", 
"neutral_social", "no_money", "positive_social", "selfharm", 
"win_money"), class = "factor"), Score = c(0.221611076, 0.206888887611111, 
0.2319999696, 0.228521740956522, 0.206187486625, 0.220866648533333, 
0.227608773956522, 0.241291721625, 0.24412006376, 0.238473741684211, 
0.2352000951, 0.233545574272727, 0.260041663875, 0.265705879882353, 
0.254225776967742, 0.250256428333333, 0.256172385758621, 0.258117654705882, 
0.218822224977778, 0.219707332097561, 0.216555555666667, 0.2150000135625, 
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0.236708313208333, 0.239999993733333, 0.240576936653846, 0.243055529055556, 
0.425774382064516, 0.355654037846154, 0.431166807733333, 0.382972372944444, 
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Is this the correct way to undertake the Shapiro test on the output of an lme

是的,结果表明,如果数据呈正态分布,观察到这些数据的概率极低(小于 < 2.2e-16)。

直方图和QQ图在这里也很有用:

...这都说明虽然它们是对称的,但与正态分布时的预期相比,这些残差的尾部非常短。