为混合模型选择哪个公式
Which formula to choose for a mixed model
编辑：我已经在 Cross Validated 上发布了以下更详细的问题，因为有人告诉我以下内容更适合发布在那里。
我正在尝试针对重复数据编写混合模型，但我很难编写公式。
我的数据库由学校不同考试的成绩组成。
每行包含一个从 0 到 100 的结果。对于每个结果，我都知道学校、考试年份和考试科目。我将学校分为两种（A 和 B）；我的objective是衡量学校的种类（A或B）是否对其结果有影响。然而，正如我所说，我对每所学校都重复了测量，因为我有 20 个学校等级，每年一个（2014 年至 2019 年），四个科目各一个。
这是我的数据示例：
Result School_ID Year Subject School_type
1 19 1 2015 math A
2 35 1 2015 english A
3 4 1 2015 history A
4 16 1 2015 philosophy A
5 55 1 2016 math A
6 62 1 2016 english A
7 74 1 2016 history A
8 66 1 2016 philosophy A
9 32 1 2017 math A
10 16 1 2017 english A
11 42 1 2017 history A
12 52 1 2017 philosophy A
13 95 1 2018 math A
14 8 1 2018 english A
15 35 1 2018 history A
16 41 1 2018 philosophy A
17 12 1 2019 math A
18 40 1 2019 english A
19 56 1 2019 history A
20 65 2 2019 philosophy B
21 12 2 2015 math B
22 23 2 2015 english B
23 45 2 2015 history B
24 90 2 2015 philosophy B
25 3 2 2016 math B
26 66 2 2016 english B
27 51 2 2016 history B
28 26 2 2016 philosophy B
29 4 2 2017 math B
因为我有重复的数据，我知道我必须使用 lmer 的混合模型（例如）。
但是，我正在努力寻找一个好的公式。
首先我尝试了这个：
Result ~ School_type * Subject + (1|Year)
但我不确定这是一个好的公式。
我也试过这个
Result ~ School_type * Subject + (Year|School_ID)
但它并没有给出任何显着的结果。起初我认为我的变量 School_type 对结果没有显着影响。这真是出乎意料。然后我想，通过将学校视为一个随机变量，这个公式抑制了学校对我结果的影响，这显然会减少 School_type 的影响，因为它与学校有关。
换句话说，我想了解学校的特点对他们成绩的影响，但如果我“压制”个人的影响，这里是学校，在随机影响中，我显然不会得到任何结果结果。
但是，我感觉我的第一个公式：
Result ~ School_type * Subject + (1|Year)
这给了我预期的结果，没有考虑到学校重复数据的事实。
根据要求，这里是 dput(my_data_frame).
structure(list(result = c(69.9, 72.4, 67.1, 84.4, 84.9, 68, 78.1,
65.1, 69.9, 77.5, 80.2, 84.7, 89.3, 82.6, 63.8, 40.8, 72.2, 71.4,
77.2, 79.9, 93.5, 65, 67.7, 91.8, 79.6, 73.4, 80.9, 85.7, 91.8,
67.1, 66.5, 84.6, 80.8, 87.3, 94, 87.8, 86.2, 36.6, 37.6, 18,
30, 34.8, 32.5, 21.9, 29, 22.7, 47.3, 70, 84.6, 60.8, 42.1, 18.6,
49.2, 33.9, 34.9, 47.1, 29.2, 34.5, 70.3, 56, 67.8, 60.9, 50.3,
40.4, 20.8, 45.4, 57.7, 65, 26.5, 40.1, 36.6, 49.1, 52.4, 22.8,
46.5, 42.4, 54.1, 51.3, 27.2, 42.9, 47.1, 61.6, 45.1, 86.5, 69.2,
58.4, 58.4, 46.8, 77, 46.9, 73.1, 50.1, 61.4, 49.2, 75, 75.4,
53.2, 71.9, 49.5, 27.4, 48.3, 51.9, 68.8, 69, 44.6, 39, 48.3,
77.5, 59.3, 70.9, 80.1, 73.5, 77.9, 57.3, 76.8, 67, 63.2, 89.8,
79.5, 70.8, 78.5, 79.4, 79.4, 80.5, 72, 68.6, 91.7, 75.6, 77.2,
77.8, 73, 85.3, 68.8, 64.6, 88.2, 76.9, 84.7, 88.5, 76.6, 81.8,
26.6, 30.9, 27.9, 33.5, 27.8, 8.7, 27.8, 31.8, 68, 23.5, 80.2,
54.8, 42.7, 46.1, 49.6, 27, 35.2, 30, 32, 62.9, 56.6, 70.2, 44.3,
39.3, 37, 24, 52.2, 44.2, 59.3, 30.4, 33.9, 33.8, 65.7, 42.8,
36.5, 43.1, 49.7, 34.3, 10.4, 47.4, 43.4, 60.8, 58.5, 93.2, 81.7,
79.4, 76.8, 66.3, 76.2, 68.2, 45, 46.7, 57.4, 89.6, 81.6, 73.8,
61.1, 43.2, 41.9, 74.8, 56.9, 71.5, 30.9, 59.6, 39.8, 76.3, 67.3,
54.5, 78, 92.6, 80.9, 81.7, 64, 75.2, 62.3, 75.9, 87.1, 73.1,
64.8, 79.3, 85.4, 81.3, 74.4, 90.6, 68.7, 71.3, 92.4, 79.5, 72.1,
86, 85.7, 90.8, 66.6, 62.8, 84.4, 77.9, 85.6, 86, 80.6, 49.4,
42.1, 28, 35.2, 32.5, 45.6, 35.6, 38.1, 38.8, 48.3, 32.2, 84.6,
61.4, 46.7, 68.7, 65, 26.7, 49.2, 55.2, 26.8, 21.8, 55.4, 43.4,
56, 44, 65.2, 42.4, 41.9, 27.6, 44, 51.1, 63, 32.9, 52.3, 44.8,
58.1, 44, 15.2, 44.2, 68.8, 53.3, 25, 57.8, 51.7, 60.8, 59.4,
88.2, 83.6, 74.2, 81.7, 64.8, 63.4, 61.1, 46.8, 47.2, 69.4, 76.3,
87.9, 78.7, 70.7, 60.8, 34.6, 42.3, 54.7, 62.1, 33.6, 51, 31.1,
72.5, 66.9, 69.4, 79.5, 80.6, 80.8, 70.5, 72.5, 63.6, 96.6, 78.4,
90.8, 75.9, 57.1, 76.2, 74.8, 59.9, 61.7, 82.6, 65.9, 73.8, 90.1,
83.2, 78, 83.5, 83.8, 87, 67.2, 60.7, 79.9, 76.1, 82, 82.2, 84.6,
48.1, 33, 13.5, 35.7, 42.6, 23.6, 35.4, 40.4, 41.6, 46.5, 24.6,
78.8, 73.6, 41.1, 68.5, 45.1, 38.6, 45, 78.4, 23.9, 35.6, 55.6,
53.3, 57.1, 63.2, 67.9, 55.2, 23.5, 41.3, 56, 50.6, 50.6, 44.2,
44.9, 46.4, 54.6, 41.5, 30, 53.6, 81, 37.2, 48, 56.8, 77.4, 59.2,
91.8, 77.3, 78.1, 80.8, 63.4, 54.6, 51.3, 63.5, 53.2, 76.3, 72.7,
79.6, 57.8, 40.2, 66, 58.3, 80.4, 72.8, 53.6, 54.2, 54, 65.3,
68.4, 79, 75.6, 81.8, 54.4, 68.5, 68.5, 77.9, 84.8, 87.1, 74.9,
64.9, 74.1, 63.8, 76, 86, 67.9, 81.8, 91.2, 81.2, 72.2, 74.9,
85.4, 90.8, 71, 64.5, 84.3, 83.3, 84.3, 85.1, 38.5, 46, 44.1,
49.3, 37.9, 26.9, 36.9, 32.3, 45.2, 51.9, 84.8, 65.9, 53.3, 43.3,
42.1, 71.4, 42.6, 29.4, 38.6, 49.5, 40.5, 63.8, 46.3, 28.7, 31.7,
57.1, 66.1, 21.8, 37.6, 49.5, 49.9, 55.7, 53.2, 53.2, 53.2, 40.2,
57.3, 64.4, 88.3, 74.2, 68.6, 53.4, 70.5, 52.4, 60.6, 49.6, 57.2,
62.6, 65.5, 66.7, 52.7, 46.7, 51.1, 53.4, 56.3, 73.7, 34.7, 65.1,
50, 54.8, 48.2, 59.8, 79, 50.1, 53, 54.8, 53.7, 52.8, 72.8, 55.4,
90, 64.1, 50.3, 2.5, 49.3, 46, 57.9, 42.2, 93.2, 53.1, 51.5,
80.7, 49.7, 70.9, 63.6, 63.2, 61.8, 59.3, 47.4, 54.9, 77.4, 69.7,
66.1, 48.8, 72.1, 59.5, 58.7, 54.3, 64.4, 83.9, 52.1, 53.1, 55.1,
63.3, 61.4, 79.5, 57.5, 68.3, 47.7, 70.4, 61, 53, 55.1, 89.2,
60.3, 50.2, 83.1, 76.9, 69.7, 64.7, 58.8, 62, 48.5, 46, 66.1,
74.1, 56, 69, 64.3, 54, 33.9, 58, 78.9, 53.4, 59.7, 59.1, 63.4,
52.2, 68.5, 56, 96.5, 53.3, 47.9, 60, 66.9, 56.6, 39.7, 93.5,
47.4, 40.1, 78.1, 63.1, 62.6, 64.3, 57.5, 56.8, 51.9, 48.8, 44.7,
56.4, 65.2, 70, 56.2, 63.2, 53.4, 44.6, 42, 56.2, 50.3, 50.2,
53.3, 47.5, 46.7, 64.1, 49.5, 71.9, 57.8, 37.2, 47.9, 46.9, 42.3,
38.4, 42.9, 46.4, 73.6, 60.6, 53.2, 61, 55.4, 41.7, 47.9, 49.6,
58.5, 63, 42.3, 65.7, 48.4, 53.5, 53.2, 51.5, 53.9, 47.8, 52.3,
58.5, 59.9, 59.9, 74, 57.8, 44.1, 61.5, 47, 59.4, 48.9, 40.5,
74.6, 56.6, 52.9, 72.2, 59.8, 50.1, 46.5, 68.7, 64.1, 64.6, 53.1,
64.8), school_ID = structure(c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L,
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31L, 32L, 33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L, 4L, 6L, 7L, 9L,
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21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L,
34L, 36L, 1L, 2L, 3L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L,
15L, 17L, 18L, 19L, 22L, 23L, 25L, 26L, 27L, 28L, 29L, 30L, 31L,
32L, 34L, 35L, 36L, 1L, 2L, 3L, 6L, 7L, 9L, 10L, 11L, 12L, 13L,
14L, 17L, 18L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L,
31L, 32L, 33L, 34L, 35L, 36L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L,
9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L, 21L,
22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L,
35L, 36L, 37L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L,
12L, 14L, 15L, 17L, 18L, 19L, 20L, 21L, 22L, 23L, 24L, 26L, 27L,
28L, 29L, 30L, 31L, 33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L, 4L,
5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 17L, 18L, 19L,
20L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L,
33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L, 4L, 6L, 7L, 8L, 9L, 10L,
11L, 12L, 13L, 14L, 15L, 17L, 18L, 19L, 20L, 22L, 23L, 24L, 26L,
27L, 28L, 29L, 30L, 31L, 33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L,
6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 17L, 18L, 19L,
22L, 23L, 24L, 26L, 27L, 28L, 29L, 30L, 31L, 33L, 34L, 35L, 36L,
37L), .Label = c("1", "2", "3", "4", "5", "6", "7", "8", "9",
"10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20",
"21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31",
"32", "33", "34", "35", "36", "37"), class = "factor"), year = structure(c(5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
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1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("2015", "2016", "2017",
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1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L), .Label = c("Math", "History", "Philosiphy",
"English"), class = "factor"), school_type = structure(c(1L,
1L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 2L, 3L, 3L, 1L, 1L, 2L,
2L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 3L,
1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 3L,
3L, 1L, 1L, 2L, 2L, 3L, 2L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L,
2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 2L,
3L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 2L,
1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 2L, 2L,
1L, 2L, 2L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 2L, 3L, 1L, 1L,
2L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 2L,
1L, 2L, 2L, 3L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 2L, 3L, 1L,
1L, 2L, 1L, 3L, 1L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 2L,
2L, 1L, 2L, 2L, 3L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 2L, 3L,
1L, 2L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L,
3L, 2L, 2L, 1L, 2L, 2L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 1L,
2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 1L, 1L,
1L, 3L, 3L, 2L, 2L, 2L, 2L, 3L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L,
1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L,
3L, 1L, 1L, 1L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 2L, 3L, 3L, 1L, 2L,
2L, 3L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 2L, 3L, 1L, 3L,
3L, 3L, 1L, 1L, 1L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 2L, 3L, 3L, 1L,
2L, 2L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 2L,
3L, 1L, 3L, 3L, 1L, 1L, 1L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 2L, 3L,
3L, 1L, 2L, 2L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L,
1L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 2L, 2L, 2L, 2L, 3L,
2L, 3L, 3L, 1L, 2L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 1L, 3L, 1L, 1L,
2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 3L, 2L,
3L, 3L, 1L, 2L, 2L, 3L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L,
1L, 2L, 3L, 1L, 3L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 3L, 2L, 3L,
3L, 1L, 2L, 2L, 3L, 1L, 2L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 1L,
3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 2L, 3L, 3L, 2L, 2L, 1L,
1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 1L,
1L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 2L, 3L, 3L, 1L, 1L, 2L,
2L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 3L,
1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 2L,
3L, 1L, 2L, 2L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 2L, 1L, 3L, 1L, 1L,
3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 2L, 3L,
2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L,
3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 2L, 2L, 1L,
2L, 2L, 3L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 2L, 3L, 1L, 2L,
1L, 3L, 1L, 1L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 1L, 2L,
2L, 3L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 1L, 2L, 3L, 1L, 2L, 1L, 3L,
1L, 1L, 3L, 1L, 3L, 3L, 3L), .Label = c("A", "B", "C"), class = "factor")), row.names = c(NA,
-664L), class = c("tbl_df", "tbl", "data.frame"))
这可能更适合 CrossValidated，因为它更多地与您应该建立什么样的模型有关，而不是如何建立，但这里是。
让我们研究一下您的模型。
result ~ school_type * subject + (1|year)
这表示结果取决于学校类型、学科及其相互作用（即学科之间的差异因学校类型而异），并且结果随着年份的随机效应而变化（即，您只感兴趣年份之间的差异，而不是年份之间的统计比较）。
问题:
- 这警告您您有一个“奇异拟合”——年内变异估计为零。这可能是因为您的样本中没有很多年，并且不一定是致命的，但确实表明该模型可能不是最优的（参见 here and here）
- 与您 hint/suggest 一样，此模型 未 考虑到每个学校有多个测量值这一事实。它假设学校内部的 schools/no 相关性没有变化，这几乎肯定是一个问题。
result ~ school_type * subject + (year|school_ID)
除了上面列出的学校 type/subject 互动之外，该模型还假设学校之间存在差异 and and 不同学校之间的年度影响差异可能是相关的（例如，在第 1 年的影响高于平均水平的学校在第 2 年的平均影响也可能高于平均水平）。
- 这个模型也是单一的
- 它（几乎）是此观察设计的最大模型；理论上你还可以添加
(1|year) 以允许跨学校一致的年度变化（当前模型只允许跨学校的年度效应变化）
- 你说“没什么重要的”。这不是我所看到的（和这不是判断你是否拥有正确模型的好方法！令人失望但完全有可能拥有正确的模型并且没有任何重要意义） .你的意思是学校类型的影响不显着（在常规p<=0.05）水平？
例如，这里是 car::Anova() 应用于此拟合的结果：
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: result
Chisq Df Pr(>Chisq)
school_type 5.3273 2 0.069692 .
subject 1030.9423 3 < 2.2e-16 ***
school_type:subject 22.1616 6 0.001132 **
请注意，在解释主效应检验时，您应该非常小心：阅读 ?car::Anova 的“详细信息”部分（并考虑设置 sum-如果您要进行类型 3 测试，则对比度为零）。
一般来说，我还建议您不要查看显着性检验，直到您决定对模型的结构感到满意为止。
我再推荐两个模型：
result ~ school_type * subject + (1|year) + (1|school_ID) + (1|year:school_ID)
这允许不同年份、不同学校之间的差异，以及独立学校内部不同年份的差异。它是明智的（并且比上面的最大模型更简约；它忽略了学校之间逐年变化的可能相关性），但它仍然给出了一个单一的模型。
result ~ school_type * subject + year + (1|school_ID/year)
这会将年份效应从随机更改为固定，当您没有很多水平来估计方差时，这是一个合理的策略。 （(1|school_ID/year) 项表示“学校之间的差异和年内差异 嵌套在学校内 ”，并且与其他两个随机效应项的组合相同以前的型号）
这个模型不是单一的。
所有模型 除了第一个 （它忽略了学校间的差异）对模型的 school_type*subject 部分给出了几乎相同的结果，这并不是真的令人惊讶，因为我们基本上只是以稍微不同的方式切分 (school × year) 的变化。
编辑：我已经在 Cross Validated 上发布了以下更详细的问题，因为有人告诉我以下内容更适合发布在那里。
我正在尝试针对重复数据编写混合模型，但我很难编写公式。
我的数据库由学校不同考试的成绩组成。 每行包含一个从 0 到 100 的结果。对于每个结果，我都知道学校、考试年份和考试科目。我将学校分为两种（A 和 B）；我的objective是衡量学校的种类（A或B）是否对其结果有影响。然而，正如我所说，我对每所学校都重复了测量，因为我有 20 个学校等级，每年一个（2014 年至 2019 年），四个科目各一个。 这是我的数据示例：
Result School_ID Year Subject School_type
1 19 1 2015 math A
2 35 1 2015 english A
3 4 1 2015 history A
4 16 1 2015 philosophy A
5 55 1 2016 math A
6 62 1 2016 english A
7 74 1 2016 history A
8 66 1 2016 philosophy A
9 32 1 2017 math A
10 16 1 2017 english A
11 42 1 2017 history A
12 52 1 2017 philosophy A
13 95 1 2018 math A
14 8 1 2018 english A
15 35 1 2018 history A
16 41 1 2018 philosophy A
17 12 1 2019 math A
18 40 1 2019 english A
19 56 1 2019 history A
20 65 2 2019 philosophy B
21 12 2 2015 math B
22 23 2 2015 english B
23 45 2 2015 history B
24 90 2 2015 philosophy B
25 3 2 2016 math B
26 66 2 2016 english B
27 51 2 2016 history B
28 26 2 2016 philosophy B
29 4 2 2017 math B
因为我有重复的数据，我知道我必须使用 lmer 的混合模型（例如）。
但是，我正在努力寻找一个好的公式。
首先我尝试了这个：
Result ~ School_type * Subject + (1|Year)
但我不确定这是一个好的公式。 我也试过这个
Result ~ School_type * Subject + (Year|School_ID)
但它并没有给出任何显着的结果。起初我认为我的变量 School_type 对结果没有显着影响。这真是出乎意料。然后我想，通过将学校视为一个随机变量，这个公式抑制了学校对我结果的影响，这显然会减少 School_type 的影响，因为它与学校有关。
换句话说，我想了解学校的特点对他们成绩的影响，但如果我“压制”个人的影响，这里是学校，在随机影响中，我显然不会得到任何结果结果。
但是，我感觉我的第一个公式：
Result ~ School_type * Subject + (1|Year)
这给了我预期的结果，没有考虑到学校重复数据的事实。
根据要求，这里是 dput(my_data_frame).
structure(list(result = c(69.9, 72.4, 67.1, 84.4, 84.9, 68, 78.1,
65.1, 69.9, 77.5, 80.2, 84.7, 89.3, 82.6, 63.8, 40.8, 72.2, 71.4,
77.2, 79.9, 93.5, 65, 67.7, 91.8, 79.6, 73.4, 80.9, 85.7, 91.8,
67.1, 66.5, 84.6, 80.8, 87.3, 94, 87.8, 86.2, 36.6, 37.6, 18,
30, 34.8, 32.5, 21.9, 29, 22.7, 47.3, 70, 84.6, 60.8, 42.1, 18.6,
49.2, 33.9, 34.9, 47.1, 29.2, 34.5, 70.3, 56, 67.8, 60.9, 50.3,
40.4, 20.8, 45.4, 57.7, 65, 26.5, 40.1, 36.6, 49.1, 52.4, 22.8,
46.5, 42.4, 54.1, 51.3, 27.2, 42.9, 47.1, 61.6, 45.1, 86.5, 69.2,
58.4, 58.4, 46.8, 77, 46.9, 73.1, 50.1, 61.4, 49.2, 75, 75.4,
53.2, 71.9, 49.5, 27.4, 48.3, 51.9, 68.8, 69, 44.6, 39, 48.3,
77.5, 59.3, 70.9, 80.1, 73.5, 77.9, 57.3, 76.8, 67, 63.2, 89.8,
79.5, 70.8, 78.5, 79.4, 79.4, 80.5, 72, 68.6, 91.7, 75.6, 77.2,
77.8, 73, 85.3, 68.8, 64.6, 88.2, 76.9, 84.7, 88.5, 76.6, 81.8,
26.6, 30.9, 27.9, 33.5, 27.8, 8.7, 27.8, 31.8, 68, 23.5, 80.2,
54.8, 42.7, 46.1, 49.6, 27, 35.2, 30, 32, 62.9, 56.6, 70.2, 44.3,
39.3, 37, 24, 52.2, 44.2, 59.3, 30.4, 33.9, 33.8, 65.7, 42.8,
36.5, 43.1, 49.7, 34.3, 10.4, 47.4, 43.4, 60.8, 58.5, 93.2, 81.7,
79.4, 76.8, 66.3, 76.2, 68.2, 45, 46.7, 57.4, 89.6, 81.6, 73.8,
61.1, 43.2, 41.9, 74.8, 56.9, 71.5, 30.9, 59.6, 39.8, 76.3, 67.3,
54.5, 78, 92.6, 80.9, 81.7, 64, 75.2, 62.3, 75.9, 87.1, 73.1,
64.8, 79.3, 85.4, 81.3, 74.4, 90.6, 68.7, 71.3, 92.4, 79.5, 72.1,
86, 85.7, 90.8, 66.6, 62.8, 84.4, 77.9, 85.6, 86, 80.6, 49.4,
42.1, 28, 35.2, 32.5, 45.6, 35.6, 38.1, 38.8, 48.3, 32.2, 84.6,
61.4, 46.7, 68.7, 65, 26.7, 49.2, 55.2, 26.8, 21.8, 55.4, 43.4,
56, 44, 65.2, 42.4, 41.9, 27.6, 44, 51.1, 63, 32.9, 52.3, 44.8,
58.1, 44, 15.2, 44.2, 68.8, 53.3, 25, 57.8, 51.7, 60.8, 59.4,
88.2, 83.6, 74.2, 81.7, 64.8, 63.4, 61.1, 46.8, 47.2, 69.4, 76.3,
87.9, 78.7, 70.7, 60.8, 34.6, 42.3, 54.7, 62.1, 33.6, 51, 31.1,
72.5, 66.9, 69.4, 79.5, 80.6, 80.8, 70.5, 72.5, 63.6, 96.6, 78.4,
90.8, 75.9, 57.1, 76.2, 74.8, 59.9, 61.7, 82.6, 65.9, 73.8, 90.1,
83.2, 78, 83.5, 83.8, 87, 67.2, 60.7, 79.9, 76.1, 82, 82.2, 84.6,
48.1, 33, 13.5, 35.7, 42.6, 23.6, 35.4, 40.4, 41.6, 46.5, 24.6,
78.8, 73.6, 41.1, 68.5, 45.1, 38.6, 45, 78.4, 23.9, 35.6, 55.6,
53.3, 57.1, 63.2, 67.9, 55.2, 23.5, 41.3, 56, 50.6, 50.6, 44.2,
44.9, 46.4, 54.6, 41.5, 30, 53.6, 81, 37.2, 48, 56.8, 77.4, 59.2,
91.8, 77.3, 78.1, 80.8, 63.4, 54.6, 51.3, 63.5, 53.2, 76.3, 72.7,
79.6, 57.8, 40.2, 66, 58.3, 80.4, 72.8, 53.6, 54.2, 54, 65.3,
68.4, 79, 75.6, 81.8, 54.4, 68.5, 68.5, 77.9, 84.8, 87.1, 74.9,
64.9, 74.1, 63.8, 76, 86, 67.9, 81.8, 91.2, 81.2, 72.2, 74.9,
85.4, 90.8, 71, 64.5, 84.3, 83.3, 84.3, 85.1, 38.5, 46, 44.1,
49.3, 37.9, 26.9, 36.9, 32.3, 45.2, 51.9, 84.8, 65.9, 53.3, 43.3,
42.1, 71.4, 42.6, 29.4, 38.6, 49.5, 40.5, 63.8, 46.3, 28.7, 31.7,
57.1, 66.1, 21.8, 37.6, 49.5, 49.9, 55.7, 53.2, 53.2, 53.2, 40.2,
57.3, 64.4, 88.3, 74.2, 68.6, 53.4, 70.5, 52.4, 60.6, 49.6, 57.2,
62.6, 65.5, 66.7, 52.7, 46.7, 51.1, 53.4, 56.3, 73.7, 34.7, 65.1,
50, 54.8, 48.2, 59.8, 79, 50.1, 53, 54.8, 53.7, 52.8, 72.8, 55.4,
90, 64.1, 50.3, 2.5, 49.3, 46, 57.9, 42.2, 93.2, 53.1, 51.5,
80.7, 49.7, 70.9, 63.6, 63.2, 61.8, 59.3, 47.4, 54.9, 77.4, 69.7,
66.1, 48.8, 72.1, 59.5, 58.7, 54.3, 64.4, 83.9, 52.1, 53.1, 55.1,
63.3, 61.4, 79.5, 57.5, 68.3, 47.7, 70.4, 61, 53, 55.1, 89.2,
60.3, 50.2, 83.1, 76.9, 69.7, 64.7, 58.8, 62, 48.5, 46, 66.1,
74.1, 56, 69, 64.3, 54, 33.9, 58, 78.9, 53.4, 59.7, 59.1, 63.4,
52.2, 68.5, 56, 96.5, 53.3, 47.9, 60, 66.9, 56.6, 39.7, 93.5,
47.4, 40.1, 78.1, 63.1, 62.6, 64.3, 57.5, 56.8, 51.9, 48.8, 44.7,
56.4, 65.2, 70, 56.2, 63.2, 53.4, 44.6, 42, 56.2, 50.3, 50.2,
53.3, 47.5, 46.7, 64.1, 49.5, 71.9, 57.8, 37.2, 47.9, 46.9, 42.3,
38.4, 42.9, 46.4, 73.6, 60.6, 53.2, 61, 55.4, 41.7, 47.9, 49.6,
58.5, 63, 42.3, 65.7, 48.4, 53.5, 53.2, 51.5, 53.9, 47.8, 52.3,
58.5, 59.9, 59.9, 74, 57.8, 44.1, 61.5, 47, 59.4, 48.9, 40.5,
74.6, 56.6, 52.9, 72.2, 59.8, 50.1, 46.5, 68.7, 64.1, 64.6, 53.1,
64.8), school_ID = structure(c(1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L,
9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L, 21L,
22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L,
35L, 36L, 37L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L,
13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L, 22L, 23L, 24L, 25L, 26L,
27L, 28L, 29L, 31L, 32L, 33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L,
4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 17L, 18L,
19L, 20L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L,
32L, 33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L, 4L, 6L, 7L, 8L, 9L,
10L, 12L, 13L, 14L, 15L, 17L, 18L, 19L, 20L, 22L, 23L, 24L, 25L,
26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L, 35L, 36L, 37L, 1L,
2L, 3L, 4L, 6L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 17L, 18L,
19L, 20L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 31L, 32L, 33L,
34L, 35L, 36L, 37L, 1L, 2L, 3L, 4L, 6L, 7L, 8L, 9L, 10L, 11L,
12L, 13L, 14L, 15L, 17L, 18L, 19L, 20L, 22L, 23L, 24L, 26L, 27L,
28L, 29L, 30L, 31L, 32L, 33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L,
4L, 5L, 6L, 7L, 8L, 9L, 10L, 12L, 13L, 14L, 15L, 17L, 18L, 19L,
20L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L,
33L, 34L, 36L, 37L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 9L, 10L, 11L,
12L, 13L, 14L, 15L, 17L, 18L, 19L, 20L, 21L, 22L, 23L, 24L, 25L,
26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L, 35L, 36L, 37L, 1L,
2L, 3L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 17L,
18L, 19L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 32L,
33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L, 4L, 6L, 7L, 8L, 9L, 10L,
11L, 12L, 13L, 14L, 15L, 17L, 18L, 19L, 20L, 21L, 22L, 23L, 24L,
25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L, 36L, 37L, 1L,
2L, 3L, 4L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 17L,
18L, 19L, 20L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L,
31L, 32L, 33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L, 4L, 6L, 7L, 9L,
10L, 11L, 12L, 13L, 14L, 15L, 17L, 18L, 19L, 22L, 23L, 24L, 26L,
27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L, 35L, 36L, 37L, 1L, 2L,
3L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 17L, 18L, 19L,
21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L,
34L, 36L, 1L, 2L, 3L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L,
15L, 17L, 18L, 19L, 22L, 23L, 25L, 26L, 27L, 28L, 29L, 30L, 31L,
32L, 34L, 35L, 36L, 1L, 2L, 3L, 6L, 7L, 9L, 10L, 11L, 12L, 13L,
14L, 17L, 18L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L,
31L, 32L, 33L, 34L, 35L, 36L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L,
9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L, 21L,
22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L, 33L, 34L,
35L, 36L, 37L, 1L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 9L, 10L, 11L,
12L, 14L, 15L, 17L, 18L, 19L, 20L, 21L, 22L, 23L, 24L, 26L, 27L,
28L, 29L, 30L, 31L, 33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L, 4L,
5L, 6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 17L, 18L, 19L,
20L, 21L, 22L, 23L, 24L, 25L, 26L, 27L, 28L, 29L, 30L, 31L, 32L,
33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L, 4L, 6L, 7L, 8L, 9L, 10L,
11L, 12L, 13L, 14L, 15L, 17L, 18L, 19L, 20L, 22L, 23L, 24L, 26L,
27L, 28L, 29L, 30L, 31L, 33L, 34L, 35L, 36L, 37L, 1L, 2L, 3L,
6L, 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 17L, 18L, 19L,
22L, 23L, 24L, 26L, 27L, 28L, 29L, 30L, 31L, 33L, 34L, 35L, 36L,
37L), .Label = c("1", "2", "3", "4", "5", "6", "7", "8", "9",
"10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20",
"21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31",
"32", "33", "34", "35", "36", "37"), class = "factor"), year = structure(c(5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L,
5L, 5L, 5L, 5L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("2015", "2016", "2017",
"2018", "2019"), class = "factor"), subject = structure(c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L), .Label = c("Math", "History", "Philosiphy",
"English"), class = "factor"), school_type = structure(c(1L,
1L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 2L, 3L, 3L, 1L, 1L, 2L,
2L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L, 1L, 2L, 3L,
1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 2L, 3L, 3L,
3L, 1L, 1L, 2L, 2L, 3L, 2L, 1L, 2L, 3L, 1L, 1L, 2L, 1L, 3L, 1L,
2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 2L, 2L,
3L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 1L, 2L, 3L, 1L, 1L, 2L,
1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 2L, 2L,
1L, 2L, 2L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 2L, 3L, 1L, 1L,
2L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 2L,
1L, 2L, 2L, 3L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 2L, 3L, 1L,
1L, 2L, 1L, 3L, 1L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L, 2L,
2L, 1L, 2L, 2L, 3L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 2L, 3L,
1L, 2L, 1L, 3L, 1L, 1L, 2L, 3L, 1L, 3L, 3L, 3L, 1L, 1L, 1L, 3L,
3L, 2L, 2L, 1L, 2L, 2L, 2L, 3L, 3L, 1L, 2L, 2L, 3L, 2L, 1L, 1L,
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1L, 1L, 3L, 1L, 3L, 3L, 3L), .Label = c("A", "B", "C"), class = "factor")), row.names = c(NA,
-664L), class = c("tbl_df", "tbl", "data.frame"))
这可能更适合 CrossValidated，因为它更多地与您应该建立什么样的模型有关，而不是如何建立，但这里是。
让我们研究一下您的模型。
result ~ school_type * subject + (1|year)
这表示结果取决于学校类型、学科及其相互作用（即学科之间的差异因学校类型而异），并且结果随着年份的随机效应而变化（即，您只感兴趣年份之间的差异，而不是年份之间的统计比较）。
问题:
- 这警告您您有一个“奇异拟合”——年内变异估计为零。这可能是因为您的样本中没有很多年，并且不一定是致命的，但确实表明该模型可能不是最优的（参见 here and here）
- 与您 hint/suggest 一样，此模型 未 考虑到每个学校有多个测量值这一事实。它假设学校内部的 schools/no 相关性没有变化，这几乎肯定是一个问题。
result ~ school_type * subject + (year|school_ID)
除了上面列出的学校 type/subject 互动之外，该模型还假设学校之间存在差异 and and 不同学校之间的年度影响差异可能是相关的（例如，在第 1 年的影响高于平均水平的学校在第 2 年的平均影响也可能高于平均水平）。
- 这个模型也是单一的
- 它（几乎）是此观察设计的最大模型；理论上你还可以添加
(1|year)以允许跨学校一致的年度变化（当前模型只允许跨学校的年度效应变化） - 你说“没什么重要的”。这不是我所看到的（和这不是判断你是否拥有正确模型的好方法！令人失望但完全有可能拥有正确的模型并且没有任何重要意义） .你的意思是学校类型的影响不显着（在常规p<=0.05）水平？
例如，这里是 car::Anova() 应用于此拟合的结果：
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: result
Chisq Df Pr(>Chisq)
school_type 5.3273 2 0.069692 .
subject 1030.9423 3 < 2.2e-16 ***
school_type:subject 22.1616 6 0.001132 **
请注意，在解释主效应检验时，您应该非常小心：阅读 ?car::Anova 的“详细信息”部分（并考虑设置 sum-如果您要进行类型 3 测试，则对比度为零）。
一般来说，我还建议您不要查看显着性检验，直到您决定对模型的结构感到满意为止。
我再推荐两个模型：
result ~ school_type * subject + (1|year) + (1|school_ID) + (1|year:school_ID)
这允许不同年份、不同学校之间的差异，以及独立学校内部不同年份的差异。它是明智的（并且比上面的最大模型更简约；它忽略了学校之间逐年变化的可能相关性），但它仍然给出了一个单一的模型。
result ~ school_type * subject + year + (1|school_ID/year)
这会将年份效应从随机更改为固定，当您没有很多水平来估计方差时，这是一个合理的策略。 （(1|school_ID/year) 项表示“学校之间的差异和年内差异 嵌套在学校内 ”，并且与其他两个随机效应项的组合相同以前的型号）
这个模型不是单一的。
所有模型 除了第一个 （它忽略了学校间的差异）对模型的 school_type*subject 部分给出了几乎相同的结果，这并不是真的令人惊讶，因为我们基本上只是以稍微不同的方式切分 (school × year) 的变化。