Emmeans连续自变量的独立性。

Question

Emmeans连续自变量的独立性。

3

我希望能够用实验中的Type_space和Type_f、Exhaustion_product以及定量变量Age来解释。

以下是我的数据：

res=structure(list(Type_space = structure(c(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, 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, 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, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 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, 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), .Label = c("", 
    "29-v1", "29-v2", "88-v1", "88-v2"), class = "factor"), Id = 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, 38L, 39L, 40L, 41L, 
    42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 
    55L, 56L, 57L, 58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 
    68L, 69L, 70L, 71L, 72L, 73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 
    81L, 82L, 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, 38L, 
    39L, 40L, 41L, 42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 
    52L, 53L, 54L, 55L, 56L, 57L, 58L, 59L, 60L, 61L, 62L, 63L, 64L, 
    65L, 66L, 67L, 68L, 69L, 70L, 71L, 72L, 73L, 74L, 75L, 76L, 77L, 
    78L, 79L, 80L, 81L, 82L, 83L, 84L, 85L, 86L, 87L, 88L, 89L, 90L, 
    91L, 92L, 93L, 94L, 95L, 96L, 97L, 98L, 99L, 100L, 101L, 102L, 
    103L, 104L, 105L, 106L, 107L, 108L, 109L, 110L, 111L, 112L, 113L, 
    114L, 115L, 116L, 117L, 118L, 119L, 120L, 121L, 122L, 123L, 124L, 
    125L, 126L, 127L, 128L, 129L, 130L, 131L, 132L, 133L, 134L, 135L, 
    136L, 137L, 138L, 139L, 140L, 141L, 142L, 143L, 144L, 145L, 146L, 
    147L, 148L, 149L, 150L, 151L, 152L, 153L, 154L, 155L, 156L, 157L, 
    158L, 159L, 160L, 161L, 162L, 163L, 164L, 165L, 166L, 167L, 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, 38L, 39L, 40L, 41L, 
    42L, 43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 
    55L, 56L, 57L, 58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 
    68L, 69L, 70L, 71L, 72L, 73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 
    81L, 82L, 83L, 84L, 85L, 86L, 87L, 88L, 89L, 90L, 91L, 92L, 93L, 
    94L, 95L, 96L, 97L, 98L, 99L, 100L, 101L, 102L, 103L, 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, 38L, 39L, 40L, 41L, 42L, 
    43L, 44L, 45L, 46L, 47L, 48L, 49L, 50L, 51L, 52L, 53L, 54L, 55L, 
    56L, 57L, 58L, 59L, 60L, 61L, 62L, 63L, 64L, 65L, 66L, 67L, 68L, 
    69L, 70L, 71L, 72L, 73L, 74L, 75L, 76L, 77L, 78L, 79L, 80L, 81L, 
    82L, 83L, 84L, 85L, 86L, 87L, 88L, 89L, 90L, 91L, 92L, 93L, 94L, 
    95L, 96L, 97L, 98L, 99L, 100L, 101L, 102L, 103L, 104L, 105L, 
    106L, 107L, 108L, 109L, 110L, 111L, 112L, 113L, 114L, 115L, 116L, 
    117L, 118L, 119L, 120L, 121L, 122L, 123L, 124L, 125L, 126L, 127L, 
    128L, 129L, 130L, 131L, 132L, 133L, 134L, 135L, 136L, 137L, 138L, 
    139L, 140L, 141L, 142L, 143L, 144L, 145L, 146L, 147L, 148L, 149L, 
    150L, 151L, 152L, 153L, 154L, 155L, 156L, 157L, 158L, 159L, 160L, 
    161L, 162L, 163L, 164L), Age = c(3, 10, 1, 5, 4, 2, 1, 8, 2, 
    13, 1, 6, 3, 5, 2, 1, 3, 8, 3, 6, 1, 3, 7, 1, 2, 2, 2, 1, 2, 
    5, 4, 1, 6, 3, 6, 8, 2, 3, 4, 7, 3, 2, 6, 2, 3, 7, 1, 5, 4, 1, 
    4, 3, 2, 3, 5, 5, 2, 1, 1, 5, 8, 7, 2, 2, 4, 3, 4, 4, 2, 2, 10, 
    7, 5, 3, 3, 5, 7, 5, 3, 4, 5, 4, 1, 8, 6, 1, 12, 1, 6, 3, 4, 
    4, 13, 5, 2, 7, 7, 20, 1, 1, 1, 7, 1, 4, 3, 8, 2, 2, 4, 1, 1, 
    2, 3, 2, 2, 6, 11, 2, 5, 5, 9, 4, 4, 2, 7, 2, 7, 10, 6, 9, 2, 
    2, 5, 11, 1, 8, 8, 4, 1, 2, 14, 11, 13, 20, 3, 3, 4, 16, 2, 6, 
    11, 9, 11, 4, 5, 6, 19, 5, 2, 6, 1, 7, 11, 3, 9, 2, 3, 6, 20, 
    8, 6, 2, 11, 18, 9, 3, 7, 3, 2, 1, 8, 3, 5, 6, 2, 5, 8, 11, 4, 
    9, 7, 2, 12, 8, 2, 9, 5, 4, 15, 5, 13, 5, 10, 13, 7, 6, 1, 12, 
    12, 10, 4, 2, 16, 7, 17, 11, 18, 4, 3, 12, 1, 3, 7, 3, 6, 5, 
    11, 10, 12, 6, 14, 8, 6, 7, 8, 5, 10, 12, 6, 13, 3, 11, 14, 7, 
    9, 9, 4, 13, 4, 2, 1, 2, 2, 1, 7, 9, 3, 10, 3, 2, 1, 3, 1, 4, 
    2, 4, 5, 4, 2, 13, 4, 1, 3, 1, 11, 4, 1, 3, 3, 7, 5, 4, 5, 6, 
    1, 2, 1, 2, 1, 6, 1, 7, 6, 9, 5, 1, 6, 3, 2, 3, 3, 8, 8, 3, 2, 
    2, 4, 2, 5, 2, 6, 8, 11, 1, 6, 3, 3, 4, 5, 5, 7, 4, 2, 7, 3, 
    3, 1, 3, 9, 5, 2, 4, 12, 1, 4, 5, 2, 7, 6, 1, 2, 6, 4, 2, 7, 
    3, 5, 5, 3, 7, 1, 5, 2, 1, 15, 3, 5, 2, 5, 13, 6, 2, 3, 5, 2, 
    8, 4, 2, 6, 7, 2, 4, 1, 13, 8, 2, 1, 2, 1, 1, 5, 2, 1, 6, 11, 
    4, 1, 7, 7, 4, 3, 5, 1, 4, 10, 1, 2, 6, 1, 11, 3, 8, 9, 2, 6, 
    8, 11, 14, 16, 4, 1, 4, 2, 1, 10, 4, 9, 3, 12, 8, 11, 8, 8, 5, 
    1, 4, 13, 3, 8, 5, 14, 3, 5, 5, 12, 1, 3, 4, 5, 2, 7, 6, 9, 6, 
    10, 5, 2, 3, 2, 10, 10, 10, 10, 10, 1, 14, 3, 5, 9, 6, 2, 2, 
    2, 4, 4, 11, 14, 2, 2, 2, 8, 7, 2, 10, 12, 1, 6, 10, 2, 3, 5, 
    10, 6, 1, 8, 4, 11, 5, 4, 3, 6, 2, 4, 6, 9, 3, 9, 11, 7, 3, 15, 
    3, 7, 3, 5, 4, 6, 9, 13, 8, 5, 7, 8, 8, 5, 10), Type_product = c("f", 
    "s", "f", "f", "f", "f", "s", "c", "s", "f", "c", "f", "f", "f", 
    "s", "s", "f", "f", "c", "f", "s", "f", "f", "s", "f", "c", "f", 
    "f", "s", "f", "f", "c", "f", "c", "f", "f", "f", "f", "f", "c", 
    "c", "c", "f", "f", "c", "c", "f", "c", "c", "c", "c", "c", "s", 
    "f", "c", "c", "c", "s", "f", "c", "f", "f", "c", "c", "f", "c", 
    "c", "c", "f", "c", "c", "c", "c", "c", "c", "c", "f", "c", "c", 
    "c", "c", "f", "c", "f", "f", "s", "f", "c", "f", "f", "f", "c", 
    "f", "f", "f", "f", "f", "s", "c", "c", "f", "f", "c", "c", "f", 
    "f", "c", "c", "f", "f", "s", "f", "c", "c", "f", "f", "f", "c", 
    "f", "f", "f", "c", "f", "f", "f", "f", "f", "f", "c", "f", "f", 
    "f", "f", "c", "s", "f", "c", "f", "f", "c", "f", "f", "f", "c", 
    "f", "c", "c", "c", "f", "f", "f", "f", "c", "c", "c", "f", "f", 
    "c", "c", "f", "c", "f", "f", "c", "c", "c", "c", "f", "f", "f", 
    "c", "c", "c", "f", "c", "f", "c", "f", "f", "f", "c", "f", "c", 
    "c", "c", "c", "c", "f", "c", "c", "c", "c", "c", "c", "c", "f", 
    "f", "f", "c", "f", "c", "f", "f", "c", "c", "f", "f", "f", "c", 
    "c", "c", "f", "c", "c", "c", "c", "c", "f", "c", "f", "f", "c", 
    "c", "f", "c", "f", "c", "f", "c", "c", "c", "f", "c", "c", "c", 
    "c", "c", "c", "c", "f", "c", "c", "f", "c", "c", "f", "f", "c", 
    "f", "f", "s", "c", "s", "c", "f", "c", "c", "s", "c", "c", "s", 
    "c", "m", "c", "c", "f", "f", "f", "f", "f", "f", "s", "f", "f", 
    "c", "c", "f", "c", "f", "f", "f", "c", "f", "f", "f", "s", "f", 
    "f", "c", "f", "c", "f", "m", "c", "c", "c", "f", "s", "f", "f", 
    "f", "c", "s", "c", "m", "f", "c", "m", "c", "f", "c", "f", "f", 
    "f", "c", "m", "f", "c", "c", "f", "c", "f", "c", "c", "c", "c", 
    "c", "f", "f", "f", "c", "m", "f", "m", "m", "c", "c", "c", "c", 
    "m", "m", "c", "f", "m", "m", "m", "m", "m", "m", "m", "m", "m", 
    "c", "c", "f", "f", "f", "f", "c", "f", "m", "f", "f", "f", "c", 
    "f", "f", "f", "c", "f", "f", "c", "c", "f", "c", "f", "c", "m", 
    "f", "c", "f", "c", "f", "f", "f", "f", "c", "c", "f", "f", "c", 
    "c", "f", "f", "f", "f", "f", "f", "c", "f", "c", "c", "f", "c", 
    "f", "f", "f", "f", "f", "f", "f", "c", "f", "c", "f", "c", "f", 
    "c", "f", "c", "f", "f", "c", "c", "c", "c", "c", "f", "f", "f", 
    "c", "f", "c", "f", "f", "c", "c", "f", "f", "c", "f", "c", "f", 
    "c", "c", "c", "f", "f", "c", "f", "c", "c", "f", "c", "f", "c", 
    "f", "c", "f", "c", "m", "c", "c", "m", "c", "c", "f", "c", "c", 
    "f", "c", "c", "c", "f", "c", "c", "m", "c", "m", "m", "c", "c", 
    "f", "c", "c", "c", "c", "m", "c", "c", "c", "m", "m", "m", "c", 
    "c", "c", "c", "m", "m", "f", "m", "m", "m", "m", "m", "m", "m", 
    "m", "m", "m", "m", "m", "m", "m", "m"), Exhaustion_product = structure(c(1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 
    3L, 3L, 3L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 
    5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
    7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
    9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 10L, 10L, 
    10L, 10L, 10L, 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, 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, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
    5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 
    6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
    7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 
    8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 
    9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 
    10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 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, 3L, 4L, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 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, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 
    10L, 10L, 10L, 10L, 10L, 10L, 10L, 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, 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, 5L, 5L, 5L, 5L, 5L, 5L, 
    5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 
    6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 
    7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 
    8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 
    9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 
    10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 
    10L), .Label = c("(0,10]", "(10,20]", "(20,30]", "(30,40]", "(40,50]", 
    "(50,60]", "(60,70]", "(70,80]", "(80,90]", "(90,100]"), class = "factor"), 
        Type_f = c(1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 
        1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 
        1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 
        0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 
        0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 
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        0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
        0, 0, 0, 0, 0, 0)), .Names = c("Type_space", "Id", "Age", 
    "Type_product", "Exhaustion_product", "Type_f"), row.names = c(1L, 
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    586L, 587L, 590L, 592L, 599L, 606L, 608L), class = "data.frame")

    an=Anova(glm(Type_f ~  Type_space  + Exhaustion_product + Age , family=binomial,data=res))
    gl=glm(Type_f ~  Type_space  + Exhaustion_product + Age  , family=binomial,data=res)
    library("emmeans")
    emmp <- emmeans( gl, pairwise ~ Exhaustion_product + Age)
    summary( emmp, infer=TRUE)

(1) 对于分类变量，结果很清晰。但是对于在广义线性模型中具有显著性的年龄变量，emmeans 生成了什么值？5.455426。这是什么意思？我该如何解释它？

 (0,10]             5.455426  0.36901411 0.2935894 Inf -0.20641061  0.94443883   1.257  0.2088

(2) 我希望能生成交互作用的图形表示 age 和 Exhaustion_product，同时这不合理。

emmip(gl, Exhaustion_product ~ Age)

编辑1 对比结果

$contrasts
 contrast                                                estimate        SE  df   asymp.LCL asymp.UCL z.ratio p.value
 (0,10],5.45542635658915 - (10,20],5.45542635658915    0.33231353 0.4078967 Inf -0.95814279 1.6227698   0.815  0.9984
 (0,10],5.45542635658915 - (20,30],5.45542635658915   -0.53694399 0.4194460 Inf -1.86393835 0.7900504  -1.280  0.9582
 (0,10],5.45542635658915 - (30,40],5.45542635658915   -0.16100309 0.4139472 Inf -1.47060101 1.1485948  -0.389  1.0000
 (0,10],5.45542635658915 - (40,50],5.45542635658915    0.40113723 0.4021403 Inf -0.87110757 1.6733820   0.998  0.9925
 (0,10],5.45542635658915 - (50,60],5.45542635658915    0.60576562 0.4106536 Inf -0.69341247 1.9049437   1.475  0.9022
 (0,10],5.45542635658915 - (60,70],5.45542635658915    1.38800301 0.4319258 Inf  0.02152631 2.7544797   3.214  0.0430
 (0,10],5.45542635658915 - (70,80],5.45542635658915    1.01677522 0.4147441 Inf -0.29534399 2.3288944   2.452  0.2952
 (0,10],5.45542635658915 - (80,90],5.45542635658915    1.99085692 0.4747929 Inf  0.48876247 3.4929514   4.193  0.0011
 (0,10],5.45542635658915 - (90,100],5.45542635658915   2.03923289 0.4745872 Inf  0.53778910 3.5406767   4.297  0.0007

- ranell

那是平均年龄。您可以指定特定的年龄集，或使用 cov.reduce = range 在最小值和最大值处进行评估，请参阅 vignette（“basics”，“emmeans”），以及其他一些文献资料。 - Russ Lenth

好的，这是均值。在我的例子中（20;30]，这意味着这是一个区间，表示年龄的平均值。我们有显著的p值和正斜率。这意味着“Type_f”随着这个区间和平均年龄的增加而增长。但是如果超过或低于这个平均值怎么办？ref_grid（gl，cov.reduce = range）实际上返回最小值和最大值，但如何使用它？谢谢 - ranell

你为什么编辑了这个问题？现在它显示了你无法观察到的输出和一个无法运行的emmip调用。所以这个问题甚至不再有意义了。 - Russ Lenth

抱歉！那只是为了显著的p值而做的。我放了原始代码。 - ranell

在你之前的评论中，每个年龄和因素水平都有完全相同的斜率。 - Russ Lenth

1个回答

网页内容由stack overflow 提供, 点击上面的

可以查看英文原文，
原文链接

- Russ Lenth · Accepted Answer

因为这个问题看起来像是一个自学的问题，我将做一个类似的例子，而不是相同的数据。但结构是相同的，有一个因子和一个协变量作为预测变量。

例子是 emmeans::fiber 数据集。它的响应变量是纤维强度，连续预测变量是直径，因子是制造它的机器。

模型：

> mod = glm(log(strength) ~ machine + diameter, data = fiber)
> summary(mod)
... (output has been abbreviated) ...
Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)  3.124387   0.068374  45.695 6.74e-14
machineB     0.026025   0.023388   1.113    0.290
machineC    -0.044593   0.025564  -1.744    0.109
diameter     0.023557   0.002633   8.946 2.22e-06

(Dispersion parameter for gaussian family taken to be 0.001356412)

使用emmeans进行分析是基于参考网格的，默认情况下，该网格由因子的所有水平和协变量的平均值组成。

> ref_grid(mod)
'emmGrid' object with variables:
    machine = A, B, C
    diameter = 24.133
Transformation: “log”

您可以在R中确认 mean（fiber $ diameter）为24.133。我强调这是直径值的平均值，而不是模型中的任何内容。

> summary(.Last.value)
 machine diameter prediction         SE  df
 A       24.13333   3.692901 0.01670845 Inf
 B       24.13333   3.718925 0.01718853 Inf
 C       24.13333   3.648307 0.01819206 Inf

Results are given on the log (not the response) scale.

这些摘要值是mod在每个machine和diameter组合中的预测结果。现在看看machine的EMM。

> emmeans(mod, "machine")
 machine   emmean         SE  df asymp.LCL asymp.UCL
 A       3.692901 0.01670845 Inf  3.660153  3.725649
 B       3.718925 0.01718853 Inf  3.685237  3.752614
 C       3.648307 0.01819206 Inf  3.612652  3.683963

Results are given on the log (not the response) scale. 
Confidence level used: 0.95

如果我们看一下diameter：

我们得到完全相同的三个预测。

> emmeans(mod, "diameter")
 diameter   emmean          SE  df asymp.LCL asymp.UCL
 24.13333 3.686711 0.009509334 Inf  3.668073  3.705349

Results are averaged over the levels of: machine 
Results are given on the log (not the response) scale. 
Confidence level used: 0.95

我们得到的EMM等于参考网格中三个预测值的平均值。需要注意的是，注释中指出结果是在机器上进行平均的，因此值得阅读该部分。

要获得模型结果的图形表示，我们可以执行以下操作：

> emmip(mod, machine ~ diameter, cov.reduce = range)

为了使参考网格使用最小值和最大直径，而不是其平均值，添加了参数cov.reduce = range。如果没有该参数，我们将得到三个点而不是三条线。这个图仍然显示模型预测，只是在更详细的数值网格上。请注意，所有三条线的斜率相同。这是因为模型是这样指定的：diameter效应被加到machine效应中。因此，每条线都有共同的斜率0.023557（请参见summary(mod)的输出）。

diameter的一个效应已经在summary(mod)中进行了测试，因此不需要事后测试。

最后一件事。该模型将log(strength)作为响应变量。如果我们想要与strength在同一比例尺下的EMMs，则只需添加type = "response"：

> emmeans(mod, "machine", type = "response")
 machine response        SE  df asymp.LCL asymp.UCL
 A       40.16118 0.6710311 Inf  38.86728  41.49815
 B       41.22008 0.7085126 Inf  39.85455  42.63239
 C       38.40960 0.6987496 Inf  37.06421  39.80384

Confidence level used: 0.95 
Intervals are back-transformed from the log scale

再次说明，结果下方的注释有助于解释输出内容。