R语言 lme4对存在三向交互作用的模型给出奇异性警告

我有一个嵌套的数据集，指定实验者（experimenter_1_2，2个值）内的细胞（no，240个值），以及三种不同治疗的治疗状态（cis_0_1，2个值;rt_0_1，取2个值;dex_dose_0_1_10_30_50_70_90_110_ug_ml，8个值）。
我正尝试用线性混合模型拟合数据：

lme4::lmer(cell_tox ~ cis_0_1 * rt_0_1 * dex_dose_0_1_10_30_50_70_90_110_ug_ml + # fixed effects: 32 treatment combinations
               + (1 | experimenter_1_2 / no),                                    # random effects: 2 experimenters
           data = df)

但我得到这个错误：

Error: number of levels of each grouping factor must be < number 
  of observations (problems: no:experimenter_1_2)

我认为，对于随机效应，不可能只有一个观察值的组（如果我的理解正确，请告诉我），所以我从分组因子中删除了no：

lme4::lmer(cell_tox ~ cis_0_1 * rt_0_1 * dex_dose_0_1_10_30_50_70_90_110_ug_ml + # fixed effects: 32 treatment combinations
               + (1 | experimenter_1_2),                                         # random effects: 2 experimenters
           data = df)

但现在我收到了这个警告，我不确定它是否可以忽略：

boundary (singular) fit: see ?isSingular

我认为原因可能是配方中的三向交互作用，但细胞 * 暴露于 * 三种处理的不同类别。那么，我应该如何处理这个警告呢？
数据：

structure(list(no = structure(1:240, .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", 
    "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", 
    "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", 
    "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", 
    "71", "72", "73", "74", "75", "76", "77", "78", "79", "80", "81", 
    "82", "83", "84", "85", "86", "87", "88", "89", "90", "91", "92", 
    "93", "94", "95", "96", "97", "98", "99", "100", "101", "102", 
    "103", "104", "105", "106", "107", "108", "109", "110", "111", 
    "112", "113", "114", "115", "116", "117", "118", "119", "120", 
    "121", "122", "123", "124", "125", "126", "127", "128", "129", 
    "130", "131", "132", "133", "134", "135", "136", "137", "138", 
    "139", "140", "141", "142", "143", "144", "145", "146", "147", 
    "148", "149", "150", "151", "152", "153", "154", "155", "156", 
    "157", "158", "159", "160", "161", "162", "163", "164", "165", 
    "166", "167", "168", "169", "170", "171", "172", "173", "174", 
    "175", "176", "177", "178", "179", "180", "181", "182", "183", 
    "184", "185", "186", "187", "188", "189", "190", "191", "192", 
    "193", "194", "195", "196", "197", "198", "199", "200", "201", 
    "202", "203", "204", "205", "206", "207", "208", "209", "210", 
    "211", "212", "213", "214", "215", "216", "217", "218", "219", 
    "220", "221", "222", "223", "224", "225", "226", "227", "228", 
    "229", "230", "231", "232", "233", "234", "235", "236", "237", 
    "238", "239", "240"), class = "factor"), cancer_treatment_modality_nt_cis_rt_cis_rt = c("NT", 
    "NT", "NT", "NT", "NT", "NT", "NT", "NT", "Cis", "Cis", "Cis", 
    "Cis", "Cis", "Cis", "Cis", "Cis", "RT", "RT", "RT", "RT", "RT", 
    "RT", "RT", "RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", 
    "Cis+RT", "Cis+RT", "Cis+RT", "NT", "NT", "NT", "NT", "NT", "NT", 
    "NT", "NT", "Cis", "Cis", "Cis", "Cis", "Cis", "Cis", "Cis", 
    "Cis", "RT", "RT", "RT", "RT", "RT", "RT", "RT", "RT", "Cis+RT", 
    "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", 
    "NT", "NT", "NT", "NT", "NT", "NT", "NT", "NT", "Cis", "Cis", 
    "Cis", "Cis", "Cis", "Cis", "Cis", "Cis", "RT", "RT", "RT", "RT", 
    "RT", "RT", "RT", "RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", 
    "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "NT", "NT", "NT", "NT", 
    "NT", "NT", "NT", "NT", "Cis", "Cis", "Cis", "Cis", "Cis", "Cis", 
    "Cis", "Cis", "RT", "RT", "RT", "RT", "RT", "RT", "RT", "RT", 
    "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", 
    "Cis+RT", "NT", "NT", "NT", "NT", "NT", "NT", "NT", "NT", "Cis", 
    "Cis", "Cis", "Cis", "Cis", "Cis", "Cis", "Cis", "RT", "RT", 
    "RT", "RT", "RT", "RT", "RT", "RT", "Cis+RT", "Cis+RT", "Cis+RT", 
    "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "NT", "NT", 
    "NT", "NT", "NT", "NT", "NT", "NT", "Cis", "Cis", "Cis", "Cis", 
    "Cis", "Cis", "Cis", "Cis", "RT", "RT", "RT", "RT", "RT", "RT", 
    "RT", "RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", 
    "Cis+RT", "Cis+RT", "Cis+RT", "NT", "NT", "NT", "NT", "NT", "NT", 
    "NT", "NT", "Cis", "Cis", "Cis", "Cis", "Cis", "Cis", "Cis", 
    "Cis", "RT", "RT", "RT", "RT", "RT", "RT", "RT", "RT", "Cis+RT", 
    "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT", 
    "NT", "NT", "NT", "NT", "Cis", "Cis", "Cis", "Cis", "RT", "RT", 
    "RT", "RT", "Cis+RT", "Cis+RT", "Cis+RT", "Cis+RT"), cis_0_1 = structure(c(1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 
    1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L), .Label = c("0", 
    "1"), class = "factor"), rt_0_1 = structure(c(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, 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, 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, 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, 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, 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, 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, 1L, 1L, 1L, 1L, 
    1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("0", 
    "1"), class = "factor"), dex_dose_0_1_10_30_50_70_90_110_ug_ml = 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, 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, 4L, 
    4L, 4L, 4L, 4L, 4L, 4L, 4L, 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, 6L, 
    6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 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, 
    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), .Label = c("0", 
    "1", "10", "30", "50", "70", "90", "110"), class = "factor"), 
        experimenter_1_2 = structure(c(1L, 1L, 1L, 1L, 2L, 2L, 2L, 
        2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 
        2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 
        2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
        2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
        1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 
        1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 
        1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 
        1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 
        2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 
        2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 
        2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 
        2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 
        1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 
        1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 
        1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 
        2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("1", "2"), class = "factor"), 
        cell_tox = c(3831, 3416.75, 2960, 3339, 4179.991, 2657.449, 
        3081.616, 3402.351, 10322.25, 11011.5, 10992.75, 11671, 9870.186, 
        11652.73, 10270.16, 13599.91, 13341.75, 13729.5, 15161.5, 
        14897, 12713.48, 14003.69, 12051.5, 11618.97, 17350.5, 17667, 
        19013.5, 17817, 14130.19, 14504.74, 15996.64, 15343.1, 2854.75, 
        2940, 3529.75, 3017.25, 3300.817, 2230.435, 2816.393, 2995.739, 
        6643.5, 7083.25, 6600.25, 8178.5, 5853.885, 6251.482, 7142.517, 
        5271.722, 9845.75, 9205.5, 9771.5, 10747.75, 8554.357, 9328.768, 
        10545.55, 10211.05, 11872, 11451.75, 11604.25, 12196.25, 
        10044.5, 11439.07, 10043.45, 12267.24, 2396, 2528.75, 3578.5, 
        2492.25, 2196.274, 2655.077, 3063.587, 2605.733, 5726.25, 
        6690, 5469.5, 7239.5, 6201.664, 5503.733, 5797.424, 5350.008, 
        9174.5, 10113.25, 9312.5, 9312, 9177.329, 8533.627, 9355.823, 
        9587.374, 11135.5, 11683.25, 9421.75, 9070.5, 10407.81, 9491.802, 
        9618.997, 10025.88, 2348.5, 2253.5, 1942, 2588, 2288.319, 
        2738.107, 2080.981, 2514.162, 4503.25, 4561.5, 4399, 4239.75, 
        3988.309, 4006.338, 4803.431, 6333.089, 8406.75, 8144.75, 
        8000.5, 7933.5, 8477.76, 7412.418, 8569.466, 7579.317, 8824, 
        8863.75, 7112.25, 8786.5, 9746.191, 8685.768, 9798.545, 9985.12, 
        2259.25, 2183.75, 2601.75, 2327, 2367.08, 3049.353, 2152.624, 
        2590.55, 3372.75, 3728.5, 3561.75, 4004, 4270.612, 4990.842, 
        4884.089, 4752.663, 8792.75, 7210.5, 7661.75, 7807, 9318.93, 
        8284.508, 8315.429, 7525.558, 8278, 7858, 8171, 7808.25, 
        9046.27, 9393.42, 9661.161, 8358.647, 2345, 2631.5, 2737.75, 
        3441, 2493.761, 2205.289, 2356.167, 2762.305, 4303.5, 3856.5, 
        3751.5, 4334.75, 4841.862, 3905.753, 4342.73, 3954.148, 8243.25, 
        7800, 7123, 8445, 8900.102, 8698.066, 8347.403, 8166.098, 
        8679.5, 8971.25, 9158.75, 7506, 8472.489, 9363.905, 9012.89, 
        9119.003, 2250.5, 2557.5, 2192.75, 3119.25, 2443.468, 2440.621, 
        1792.035, 2482.373, 3079, 3666.25, 3694, 3493, 2966.797, 
        3649.545, 4787.299, 3615.383, 7765, 7076.75, 7710, 7961.5, 
        7288.737, 8126.394, 8749.014, 8084.581, 9296, 8396, 8145.75, 
        8139.75, 8519.924, 8898.345, 8556.817, 7979.523, 2460.074, 
        2006.016, 1627.871, 2402.19, 2607.156, 2027.841, 3266.655, 
        2753.764, 9234.954, 8680.147, 8561.736, 13133.71, 8656.254, 
        9102.84, 8920.481, 11059.25)), class = "data.frame", row.names = c(NA, 
    240L))

是的，您是正确的，因为如果每个水平仅存在一个观测，则通常无法拟合随机效应。删除no项后的奇异拟合很可能是由于随机截距仅具有两个水平。如果要拟合随机截距，建议因子至少具有六个水平。请参见此处的讨论：https://stats.stackexchange.com/questions/37647/what-is-the-minimum-recommended-number-of-groups-for-a-random-effects-factor
如果您查看模型中的随机效应，您会发现它无法估计随机截距，并且将其报告为零。

m1 <- lmer(cell_tox ~ cis_0_1*rt_0_1*dex_dose_0_1_10_30_50_70_90_110_ug_ml # Fixed:  32 different combinations
           + (1 | experimenter_1_2),                          # Random: 2 Experiment
           data = df)

summary(m1)
Linear mixed model fit by REML ['lmerMod']
Formula: cell_tox ~ cis_0_1 * rt_0_1 * dex_dose_0_1_10_30_50_70_90_110_ug_ml +      (1 | experimenter_1_2)
   Data: df

REML criterion at convergence: 3421.4

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0311 -0.5180 -0.0499  0.4395  4.1717 

Random effects:
 Groups           Name        Variance Std.Dev.
 experimenter_1_2 (Intercept)      0     0.0   
 Residual                     599882   774.5   
Number of obs: 240, groups:  experimenter_1_2, 2

Fixed effects:
                                                          Estimate Std. Error t value
(Intercept)                                                 3358.5      273.8  12.265
cis_0_11                                                    7815.3      387.3  20.181
rt_0_11                                                    10081.2      387.3  26.032
dex_dose_0_1_10_30_50_70_90_110_ug_ml1                      -397.9      387.3  -1.027
dex_dose_0_1_10_30_50_70_90_110_ug_ml10                     -669.0      387.3  -1.728
dex_dose_0_1_10_30_50_70_90_110_ug_ml30                    -1014.3      387.3  -2.619
dex_dose_0_1_10_30_50_70_90_110_ug_ml50                     -917.1      387.3  -2.368
dex_dose_0_1_10_30_50_70_90_110_ug_ml70                     -736.9      387.3  -1.903
dex_dose_0_1_10_30_50_70_90_110_ug_ml90                     -948.7      387.3  -2.450
dex_dose_0_1_10_30_50_70_90_110_ug_ml110                   -1234.5      474.3  -2.603
cis_0_11:rt_0_11                                           -4777.1      547.7  -8.723
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml1            -4147.8      547.7  -7.574
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml10           -4507.6      547.7  -8.230
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml30           -5555.2      547.7 -10.143
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml50           -6061.1      547.7 -11.067
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml70           -6275.5      547.7 -11.459
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml90           -6606.2      547.7 -12.062
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml110          -7275.5      670.8 -10.847
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml1             -3265.5      547.7  -5.963
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml10            -3449.9      547.7  -6.299
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml30            -4359.8      547.7  -7.961
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml50            -4408.0      547.7  -8.049
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml70            -4487.4      547.7  -8.194
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml90            -4645.7      547.7  -8.483
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml110           -2302.6      670.8  -3.433
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml1     2698.2      774.5   3.484
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml10    2255.5      774.5   2.912
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml30    3426.7      774.5   4.424
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml50    3480.2      774.5   4.493
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml70    3807.5      774.5   4.916
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml90    4214.3      774.5   5.441
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml110   3769.4      948.6   3.974

Correlation matrix not shown by default, as p = 32 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')

由于估计值为零，因此应与不含该项的模型相同。我们可以拟合线性模型，将随机截距作为固定效应。混合模型可能不适用于此数据。

m2 <- lm(cell_tox ~ cis_0_1*rt_0_1*dex_dose_0_1_10_30_50_70_90_110_ug_ml +
         experimenter_1_2,
         data = df)

summary(m2)
Call:
lm(formula = cell_tox ~ cis_0_1 * rt_0_1 * dex_dose_0_1_10_30_50_70_90_110_ug_ml + 
    experimenter_1_2, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-2304.9  -415.1   -49.3   351.8  3231.1 

Coefficients:
                                                          Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                3401.27     278.90  12.196  < 2e-16 ***
cis_0_11                                                   7815.29     387.56  20.166  < 2e-16 ***
rt_0_11                                                   10081.15     387.56  26.012  < 2e-16 ***
dex_dose_0_1_10_30_50_70_90_110_ug_ml1                     -397.88     387.56  -1.027 0.305793    
dex_dose_0_1_10_30_50_70_90_110_ug_ml10                    -669.00     387.56  -1.726 0.085805 .  
dex_dose_0_1_10_30_50_70_90_110_ug_ml30                   -1014.32     387.56  -2.617 0.009519 ** 
dex_dose_0_1_10_30_50_70_90_110_ug_ml50                    -917.10     387.56  -2.366 0.018887 *  
dex_dose_0_1_10_30_50_70_90_110_ug_ml70                    -736.92     387.56  -1.901 0.058631 .  
dex_dose_0_1_10_30_50_70_90_110_ug_ml90                    -948.71     387.56  -2.448 0.015201 *  
dex_dose_0_1_10_30_50_70_90_110_ug_ml110                  -1191.74     477.48  -2.496 0.013344 *  
experimenter_1_22                                           -85.49     103.58  -0.825 0.410109    
cis_0_11:rt_0_11                                          -4777.13     548.09  -8.716 9.37e-16 ***
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml1           -4147.79     548.09  -7.568 1.23e-12 ***
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml10          -4507.55     548.09  -8.224 2.15e-14 ***
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml30          -5555.15     548.09 -10.136  < 2e-16 ***
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml50          -6061.06     548.09 -11.059  < 2e-16 ***
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml70          -6275.54     548.09 -11.450  < 2e-16 ***
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml90          -6606.19     548.09 -12.053  < 2e-16 ***
cis_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml110         -7275.47     671.27 -10.838  < 2e-16 ***
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml1            -3265.52     548.09  -5.958 1.08e-08 ***
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml10           -3449.88     548.09  -6.294 1.81e-09 ***
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml30           -4359.79     548.09  -7.955 1.16e-13 ***
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml50           -4408.02     548.09  -8.043 6.70e-14 ***
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml70           -4487.39     548.09  -8.187 2.71e-14 ***
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml90           -4645.72     548.09  -8.476 4.36e-15 ***
rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml110          -2302.56     671.27  -3.430 0.000728 ***
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml1    2698.17     775.11   3.481 0.000609 ***
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml10   2255.53     775.11   2.910 0.004010 ** 
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml30   3426.70     775.11   4.421 1.59e-05 ***
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml50   3480.19     775.11   4.490 1.18e-05 ***
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml70   3807.49     775.11   4.912 1.83e-06 ***
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml90   4214.30     775.11   5.437 1.52e-07 ***
cis_0_11:rt_0_11:dex_dose_0_1_10_30_50_70_90_110_ug_ml110  3769.38     949.32   3.971 9.89e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 775.1 on 207 degrees of freedom
Multiple R-squared:  0.9626,    Adjusted R-squared:  0.9569 
F-statistic: 166.6 on 32 and 207 DF,  p-value: < 2.2e-16

R语言 lme4对存在三向交互作用的模型给出奇异性警告

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