我有时会发现来自glmer，包lme4的我的GLMM在调用其摘要时会显示以下警告消息：
Warning messages:
1: In vcov.merMod(object, use.hessian = use.hessian) :
variance-covariance matrix computed from finite-difference Hessian is
not positive definite or contains NA values: falling back to var-cov estimated from RX
2: In vcov.merMod(object, correlation = correlation, sigm = sig) :
variance-covariance matrix computed from finite-difference Hessian is
not positive definite or contains NA values: falling back to var-cov estimated from RX
我在Stackoverflow上找到的类似问题是指其他函数，而不是glmer，而LME4 Wiki也没有详细说明。在this问题中，问题在解决了那种错误消息之前得到了解决，here讨论的重点是特定模型，而不是警告信息的含义。
所以问题是：我应该担心这个消息，还是可以，因为它只是一个警告，而不是错误，正如它所说，它是＆＃34;回到从RX＆估计的var-cov ＃34; （无论RX是什么）无论如何。
有趣的是，虽然摘要说明模型未能收敛，但我没有得到红色的通常收敛警告。
这是一个（最小）数据集：
testdata=structure(list(Site = 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, 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, 6L, 6L, 6L, 6L, 6L, 6L, 6L,
6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L), .Label = c("EO1", "EO2",
"EO3", "EO4", "EO5", "EO6"), class = "factor"), Treatment = structure(c(1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 1L,
1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L), .Label = c("control",
"no ants", "no birds", "no birds no ants"), class = "factor"),
Tree = structure(c(2L, 3L, 4L, 16L, 12L, 13L, 14L, 15L, 5L,
6L, 7L, 8L, 1L, 9L, 10L, 11L, 28L, 29L, 30L, 31L, 17L, 25L,
26L, 27L, 18L, 19L, 20L, 32L, 21L, 22L, 23L, 24L, 33L, 41L,
42L, 43L, 37L, 38L, 39L, 40L, 44L, 45L, 46L, 47L, 34L, 35L,
36L, 48L, 49L, 57L, 58L, 59L, 50L, 51L, 52L, 64L, 53L, 54L,
55L, 56L, 60L, 61L, 62L, 63L, 66L, 67L, 68L, 80L, 69L, 70L,
71L, 72L, 76L, 77L, 78L, 79L, 65L, 73L, 74L, 75L, 82L, 83L,
84L, 96L, 92L, 93L, 94L, 95L, 85L, 86L, 87L, 88L, 81L, 89L,
90L, 91L), .Label = c("EO1 1", "EO1 10", "EO1 11", "EO1 12",
"EO1 13", "EO1 14", "EO1 15", "EO1 16", "EO1 2", "EO1 3",
"EO1 4", "EO1 5", "EO1 6", "EO1 7", "EO1 8", "EO1 9", "EO2 1",
"EO2 10", "EO2 11", "EO2 12", "EO2 13", "EO2 14", "EO2 15",
"EO2 16", "EO2 2", "EO2 3", "EO2 4", "EO2 5", "EO2 6", "EO2 7",
"EO2 8", "EO2 9", "EO3 1", "EO3 10", "EO3 11", "EO3 12",
"EO3 13", "EO3 14", "EO3 15", "EO3 16", "EO3 2", "EO3 3",
"EO3 4", "EO3 5", "EO3 6", "EO3 7", "EO3 8", "EO3 9", "EO4 1",
"EO4 10", "EO4 11", "EO4 12", "EO4 13", "EO4 14", "EO4 15",
"EO4 16", "EO4 2", "EO4 3", "EO4 4", "EO4 5", "EO4 6", "EO4 7",
"EO4 8", "EO4 9", "EO5 1", "EO5 10", "EO5 11", "EO5 12",
"EO5 13", "EO5 14", "EO5 15", "EO5 16", "EO5 2", "EO5 3",
"EO5 4", "EO5 5", "EO5 6", "EO5 7", "EO5 8", "EO5 9", "EO6 1",
"EO6 10", "EO6 11", "EO6 12", "EO6 13", "EO6 14", "EO6 15",
"EO6 16", "EO6 2", "EO6 3", "EO6 4", "EO6 5", "EO6 6", "EO6 7",
"EO6 8", "EO6 9"), class = "factor"), predators_trunk = c(7L,
10L, 9L, 15L, 18L, 11L, 5L, 7L, 15L, 12L, 6L, 12L, 7L, 13L,
24L, 17L, 3L, 0L, 0L, 2L, 4L, 3L, 0L, 6L, 2L, 3L, 5L, 1L,
5L, 12L, 18L, 15L, 7L, 0L, 5L, 1L, 17L, 7L, 13L, 19L, 7L,
3L, 5L, 10L, 11L, 7L, 13L, 7L, 7L, 0L, 4L, 2L, 5L, 7L, 4L,
7L, 8L, 7L, 9L, 20L, 13L, 2L, 12L, 7L, 0L, 7L, 2L, 2L, 2L,
4L, 17L, 2L, 3L, 1L, 1L, 1L, 11L, 1L, 1L, 8L, 8L, 18L, 5L,
6L, 6L, 5L, 6L, 5L, 9L, 2L, 8L, 13L, 13L, 5L, 3L, 5L), pH_H2O = c(4.145,
4.145, 4.145, 4.145, 4.1825, 4.1825, 4.1825, 4.1825, 4.1325,
4.1325, 4.1325, 4.1325, 4.14125, 4.14125, 4.14125, 4.14125,
4.265, 4.265, 4.265, 4.265, 4.21, 4.21, 4.21, 4.21, 4.18375,
4.18375, 4.18375, 4.18375, 4.09625, 4.09625, 4.09625, 4.09625,
4.1575, 4.1575, 4.1575, 4.1575, 4.1125, 4.1125, 4.1125, 4.1125,
4.20875, 4.20875, 4.20875, 4.20875, 3.97125, 3.97125, 3.97125,
3.97125, 4.025, 4.025, 4.025, 4.025, 4.005, 4.005, 4.005,
4.005, 4.04, 4.04, 4.04, 4.04, 4.03125, 4.03125, 4.03125,
4.03125, 4.4575, 4.4575, 4.4575, 4.4575, 4.52, 4.52, 4.52,
4.52, 4.505, 4.505, 4.505, 4.505, 4.34875, 4.34875, 4.34875,
4.34875, 4.305, 4.305, 4.305, 4.305, 4.32, 4.32, 4.32, 4.32,
4.35, 4.35, 4.35, 4.35, 4.445, 4.445, 4.445, 4.445), ant_mean_abundance = c(53.85714,
53.85714, 53.85714, 53.85714, 24.28571, 24.28571, 24.28571,
24.28571, 45.5, 45.5, 45.5, 45.5, 51.14286, 51.14286, 51.14286,
51.14286, 66.28571, 66.28571, 66.28571, 66.28571, 76.5, 76.5,
76.5, 76.5, 65.71429, 65.71429, 65.71429, 65.71429, 8.642857,
8.642857, 8.642857, 8.642857, 109.3571, 109.3571, 109.3571,
109.3571, 25.14286, 25.14286, 25.14286, 25.14286, 101.3571,
101.3571, 101.3571, 101.3571, 31.78571, 31.78571, 31.78571,
31.78571, 78.64286, 78.64286, 78.64286, 78.64286, 93.28571,
93.28571, 93.28571, 93.28571, 63.14286, 63.14286, 63.14286,
63.14286, 67.14286, 67.14286, 67.14286, 67.14286, 44.0625,
44.0625, 44.0625, 44.0625, 23.875, 23.875, 23.875, 23.875,
95.8125, 95.8125, 95.8125, 95.8125, 49.125, 49.125, 49.125,
49.125, 57, 57, 57, 57, 38.125, 38.125, 38.125, 38.125, 40.6875,
40.6875, 40.6875, 40.6875, 22, 22, 22, 22), bird_activity = c(153.24,
153.24, 153.24, 153.24, 153.24, 153.24, 153.24, 153.24, 0,
0, 0, 0, 0, 0, 0, 0, 240.96, 240.96, 240.96, 240.96, 240.96,
240.96, 240.96, 240.96, 0, 0, 0, 0, 0, 0, 0, 0, 154.54, 154.54,
154.54, 154.54, 154.54, 154.54, 154.54, 154.54, 0, 0, 0,
0, 0, 0, 0, 0, 107.68, 107.68, 107.68, 107.68, 107.68, 107.68,
107.68, 107.68, 0, 0, 0, 0, 0, 0, 0, 0, 172.42, 172.42, 172.42,
172.42, 172.42, 172.42, 172.42, 172.42, 0, 0, 0, 0, 0, 0,
0, 0, 113.8, 113.8, 113.8, 113.8, 113.8, 113.8, 113.8, 113.8,
0, 0, 0, 0, 0, 0, 0, 0)), .Names = c("Site", "Treatment",
"Tree", "predators_trunk", "pH_H2O", "ant_mean_abundance", "bird_activity"
), class = "data.frame", row.names = c(NA, -96L))
以下是导致警告的代码：
library(lme4)
summary(glmer.nb(predators_trunk ~ scale(ant_mean_abundance) + scale(bird_activity) + scale(pH_H2O) + (1 | Site/Treatment), testdata, na.action = na.fail))
summary(glmer(predators_trunk ~ scale(ant_mean_abundance) + scale(bird_activity) + scale(pH_H2O) + (1 | Site/Treatment), testdata, family = negative.binomial(theta = 4.06643400243645), na.action = na.fail))
有趣的是，glmer.nb的摘要不会产生任何警告，但使用glmer估算的theta对glmer.nb的调用确实给了我警告。后者是通过在相应的dredge完整模型上使用glmer.nb（MuMIn）生成的模型调用。
答案 0 :(得分：4)
此警告表示您的标准错误估算值可能不准确。但正如所有警告一样，很难确切知道，最好的办法是尽量交叉检查是否可以。
在这种情况下，我将glmer.nb和glmer保存为g1和g2。您可以看到估计值（点估计值，SE，Z值......）已经发生了一些变化，但不是很多，所以至少应该让您放心。
printCoefmat(coef(summary(g1)),digits=2)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.844 0.111 16.7 <2e-16 ***
scale(ant_mean_abundance) -0.347 0.077 -4.5 7e-06 ***
scale(bird_activity) -0.122 0.076 -1.6 0.107
scale(pH_H2O) -0.275 0.104 -2.6 0.008 **
> printCoefmat(coef(summary(g2)),digits=2)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.846 0.108 17.1 <2e-16 ***
scale(ant_mean_abundance) -0.347 0.077 -4.5 6e-06 ***
scale(bird_activity) -0.122 0.075 -1.6 0.102
scale(pH_H2O) -0.275 0.102 -2.7 0.007 **
我在Github（lme4分支上有一个test_mods的开发版本，希望很快就会集成到主分支中：如果你想安装它，你可以使用devtools::install_github("lme4/lme4",ref="test_mods")）允许您为标准错误选择更准确（但更慢）的计算：这使我们回到（几乎）与glmer.nb相同的标准错误。
g3 <- update(g2, control=glmerControl(deriv.method="Richardson"))
printCoefmat(coef(summary(g3)),digits=2)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.846 0.111 16.7 <2e-16 ***
scale(ant_mean_abundance) -0.347 0.077 -4.5 6e-06 ***
scale(bird_activity) -0.122 0.076 -1.6 0.106
scale(pH_H2O) -0.275 0.104 -2.6 0.008 **
all.equal(coef(summary(g1))[,"Std. Error"],
coef(summary(g3))[,"Std. Error"])
[1] "Mean relative difference: 0.001597978"
glmmTMB包（在Github上）也提供了几乎相同的结果：
library(glmmTMB)
g5 <- glmmTMB(predators_trunk ~ scale(ant_mean_abundance) +
scale(bird_activity) + scale(pH_H2O) +
(1 | Site/Treatment), testdata,
family=nbinom2)
printCoefmat(coef(summary(g5))[["cond"]],digits=2)
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.852 0.110 16.8 <2e-16 ***
scale(ant_mean_abundance) -0.348 0.077 -4.5 7e-06 ***
scale(bird_activity) -0.123 0.076 -1.6 0.106
scale(pH_H2O) -0.276 0.105 -2.6 0.008 **