lme4 glmer 中的缩放预测变量不会解决特征值警告；替代优化也没有
Scaling predictors in lme4 glmer doesn't resolve eigenvalue warnings; neither does alternative optimization
我正在使用 R 中的 lme4 的 glmer 函数分析数据（包括在下面）。
我正在构建的模型由一个泊松分布响应变量（obs）、一个随机因子（area）、一个连续偏移量（duration）、五个连续固定效应（can_perc、can_n、time、temp、cloud_cover) 和一个二项式固定效应因子 (burnt)。
在拟合模型之前，我检查了共线性并删除了所有共线性变量。
初始模型为：
q1 = glmer(obs ~ can_perc + can_n + time * temp +
cloud_cover + factor(burnt) + (1|area) + offset(dat$duration),
data=dat, family=poisson, na.action = na.fail)
（注意：我需要将 na.action 指定为 'na.fail'，因为我想稍后 dredge() 模型，这是必需的。）
运行 模型给出以下警告：
"Hessian is numerically singular: parameters are not uniquely determined"
在模型的类似变体中，我也收到了警告：
"In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model is nearly unidentifiable: large eigenvalue ratio - Rescale variables?"
根据我对此处 https://rdrr.io/cran/lme4/man/troubleshooting.html 和其他地方建议的有限理解，这两个警告都反映了一个类似的问题，即 Hessian（逆曲率矩阵）具有较大的特征值，表明（在数值公差范围内）表面在某个方向上是完全平坦的。
根据警告和 link 中的建议，我使用 scale() 重新调整了所有连续预测变量。我还缩放了偏移量变量（我尝试了缩放和不缩放这个变量）。带有缩放预测变量的模型在这里：
q2 = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp +
s.cloud_cover + factor(burnt) + (1|area) +
offset(dat$s.duration),
data=dat, family=poisson, na.action = na.fail)
但是我还没有逃过特征值！缩放模型给出了两个警告：
"unable to evaluate scaled gradient"
"Model failed to converge: degenerate Hessian with 1 negative eigenvalues"
我在网上搜索了很多，但找不到另一个 case/solution 来说明如何在预测变量缩放后处理特征值问题，除了检查模型是否没有被错误指定。
尝试解决 warnings/improve 优化：
基于这些 pages/documents：
https://cran.r-project.org/web/packages/lme4/lme4.pdf
https://rdrr.io/cran/lme4/man/isSingular.html
https://stats.stackexchange.com/questions/242109/model-failed-to-converge-warning-in-lmer
和其他人，
我有：
检查了模型规格和数据是否有错误（none 我能看到 - 我是不是漏掉了什么？）
使用 is_singular(x, tol = 1e-05) 检查奇异性（这个函数调用不知何故从 isSingular() 演变为当前形式？）：所有模型都给出 FALSE。
用converge_ok(q2, tolerance = 0.001)检查了收敛性措施：所有模型都给出FALSE，除非我大幅增加公差；然而，它们在收敛措施上确实存在很大差异。
尝试了不同的optimizers/model估计方法如下：
- a)
glmerControl(optimizer = "bobyqa") and glmerControl(optimizer ="Nelder_Mead")
- b)
glmerControl(optimizer ='optimx', optCtrl=list(method='nlminb'))
- c) bobyqa、Nelder_Mead、optimx.nlminb、optimx.L-BFGS-B、nloptwrap.NLOPT_LN_NELDERMEAD、nloptwrap.NLOPT_LN_BOBYQA 和 nmkbw 优化器，使用
all_fit() 来自 optimx 包的函数。
代码如下：
# singularity and convergence for first two models:
is_singular(s1, tol = 1e-05) # FALSE (a good thing?)
converge_ok(s1, tol = 1e-05) # FALSE (a bad thing?) 0.0259109730912352
is_singular(s2, tol = 1e-05) # FALSE (a good thing?)
converge_ok(s2, tol = 1e-05) # FALSE (a bad thing?) 0.0023434329028163
# I looked at singularity and converge measures for the others below, but omitted for brevity.
# Alternate optimisations for q1:
q1.bobyqa = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
# Warning 1: unable to evaluate scaled gradient
# Warning 2: Model failed to converge: degenerate Hessian with 1 negative eigenvalues
q1.neldermead = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer ="Nelder_Mead", optCtrl = list(maxfun = 2e5)))
# Warning: unable to evaluate scaled gradient Hessian is numerically singular: parameters are not uniquely determined
q1.nlminb = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer ='optimx', optCtrl=list(method='nlminb')))
# Warning: Parameters or bounds appear to have different scalings. This can cause poor performance in optimization.
# It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.convergence code 9999 from optimxError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, : (maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate
all_fit(q1)
# Alternate optimisations for q2:
q2.bobyqa = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover + factor(burnt) + (1|area) + offset(dat$s.duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
# Warning 1: unable to evaluate scaled gradient
# Warning 2: Model failed to converge: degenerate Hessian with 1 negative eigenvalues
q2.neldermead = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover + factor(burnt) + (1|area) + offset(dat$s.duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer ="Nelder_Mead", optCtrl = list(maxfun = 2e5)))
# Warning: unable to evaluate scaled gradient Hessian is numerically singular: parameters are not uniquely determined
q2.nlminb = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover + factor(burnt) + (1|area) + offset(dat$s.duration), data=dat, family=poisson, na.action = na.fail, control = glmerControl(optimizer ='optimx', optCtrl=list(method='nlminb')))
# Warning: Model is nearly unidentifiable: large eigenvalue ratio - Rescale variables?
all_fit(q2)
以上代码的输出，对于未缩放模型 (q1)：
is_singular(s1, tol = 1e-05) # FALSE (a good thing?)
[1] FALSE
converge_ok(s1, tol = 1e-05) # FALSE (a bad thing?) 0.0259109730912352
0.0259109730912352
FALSE
is_singular(s2, tol = 1e-05) # FALSE (a good thing?)
[1] FALSE
alternate optimisations for original model:
q1.bobyqa = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues
alternate optimisations for original model:
q1.bobyqa = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues
q1.neldermead = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer ="Nelder_Mead", optCtrl = list(maxfun = 2e5)))
unable to evaluate scaled gradient Hessian is numerically singular: parameters are not uniquely determined
all_fit(q1)
bobyqa. : unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues[OK]
Nelder_Mead. : unable to evaluate scaled gradient Hessian is numerically singular: parameters are not uniquely determined[OK]
optimx.nlminb : Parameters or bounds appear to have different scalings.
This can cause poor performance in optimization.
It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.convergence code 9999 from optimxParameters or bounds appear to have different scalings.
This can cause poor performance in optimization.
It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.convergence code 9999 from optimx[ERROR]
optimx.L-BFGS-B : Parameters or bounds appear to have different scalings.
This can cause poor performance in optimization.
It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.convergence code 9999 from optimxParameters or bounds appear to have different scalings.
This can cause poor performance in optimization.
It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.convergence code 9999 from optimx[ERROR]
nloptwrap.NLOPT_LN_NELDERMEAD : [ERROR]
nloptwrap.NLOPT_LN_BOBYQA : [ERROR]
nmkbw. : [ERROR]
$`bobyqa.`
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1 | area) + offset(dat$duration)
Data: dat
AIC BIC logLik deviance df.resid
311.0473 330.3356 -146.5237 293.0473 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 1.992
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept) can_perc can_n time temp
-67.4998 -1.3180 0.0239 4.8025 1.7793
cloud_cover factor(burnt)unburnt time:temp
-0.3813 18.5676 -0.1748
convergence code 0; 2 optimizer warnings; 0 lme4 warnings
$Nelder_Mead.
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1 | area) + offset(dat$duration)
Data: dat
AIC BIC logLik deviance df.resid
311.0473 330.3356 -146.5237 293.0473 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 1.992
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept)
can_perc can_n time temp
-67.48057 -1.31791 0.02389 4.80463 1.78012
cloud_cover factor(burnt)unburnt time:temp
-0.38118 18.52637 -0.17483
convergence code 0; 2 optimizer warnings; 0 lme4 warnings
$optimx.nlminb
<std::runtime_error in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): (maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate>
$`optimx.L-BFGS-B`
<std::runtime_error in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): (maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate>
$nloptwrap.NLOPT_LN_NELDERMEAD
<simpleError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): Downdated VtV is not positive definite>
$nloptwrap.NLOPT_LN_BOBYQA
<simpleError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): Downdated VtV is not positive definite>
$nmkbw.
<std::runtime_error in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): (maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate>
上述代码的输出，对于缩放模型 (q2)：
alternate optimisations for q2:
q2.bobyqa = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover + factor(burnt) + (1|area) + offset(dat$s.duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
Model is nearly unidentifiable: large eigenvalue ratio - Rescale variables?
q2.neldermead = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover + factor(burnt) + (1|area) + offset(dat$s.duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer ="Nelder_Mead", optCtrl = list(maxfun = 2e5)))
unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues
all_fit(q2)
bobyqa. : Model is nearly unidentifiable: large eigenvalue ratio
- Rescale variables?[OK]
Nelder_Mead. : unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues[OK]
optimx.nlminb : Model is nearly unidentifiable: large eigenvalue ratio
- Rescale variables?[OK]
optimx.L-BFGS-B : unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues[OK]
nloptwrap.NLOPT_LN_NELDERMEAD : [ERROR]
nloptwrap.NLOPT_LN_BOBYQA : [ERROR]
nmkbw. : [ERROR]
$`bobyqa.`
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: n_shreiberi ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover +
factor(burnt) + (1 | area) + offset(dat$s.duration)
Data: dat
AIC BIC logLik deviance df.resid
316.8412 336.1294 -149.4206 298.8412 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 2.523
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept) s.can_perc s.can_n s.time s.temp
-18.19816 -0.22152 0.45839 0.05239 -0.24983
s.cloud_cover factor(burnt)unburnt s.time:s.temp
-0.19691 17.92390 -0.13948
convergence code 0; 1 optimizer warnings; 0 lme4 warnings
$Nelder_Mead.
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: n_shreiberi ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover +
factor(burnt) + (1 | area) + offset(dat$s.duration)
Data: dat
AIC BIC logLik deviance df.resid
316.8408 336.1290 -149.4204 298.8408 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 2.524
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept) s.can_perc s.can_n s.time s.temp
-19.29632 -0.22153 0.45840 0.05241 -0.24990
s.cloud_cover factor(burnt)unburnt s.time:s.temp
-0.19692 19.02091 -0.13949
convergence code 0; 2 optimizer warnings; 0 lme4 warnings
$optimx.nlminb
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: n_shreiberi ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover +
factor(burnt) + (1 | area) + offset(dat$s.duration)
Data: dat
AIC BIC logLik deviance df.resid
316.8412 336.1294 -149.4206 298.8412 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 2.523
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept) s.can_perc s.can_n s.time s.temp
-18.23626 -0.22152 0.45839 0.05239 -0.24983
s.cloud_cover factor(burnt)unburnt s.time:s.temp
-0.19691 17.96199 -0.13948
convergence code 0; 1 optimizer warnings; 0 lme4 warnings
$`optimx.L-BFGS-B`
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: n_shreiberi ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover +
factor(burnt) + (1 | area) + offset(dat$s.duration)
Data: dat
AIC BIC logLik deviance df.resid
316.8412 336.1294 -149.4206 298.8412 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 2.524
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept) s.can_perc s.can_n s.time s.temp
-18.23581 -0.22155 0.45841 0.05242 -0.24997
s.cloud_cover factor(burnt)unburnt s.time:s.temp
-0.19694 17.96246 -0.13943
convergence code 0; 2 optimizer warnings; 0 lme4 warnings
$nloptwrap.NLOPT_LN_NELDERMEAD
<simpleError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): Downdated VtV is not positive definite>
$nloptwrap.NLOPT_LN_BOBYQA
<simpleError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): Downdated VtV is not positive definite>
$nmkbw.
<simpleError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): Downdated VtV is not positive definite>
数据：
数据集可在此处获得link：
https://www.dropbox.com/s/ud50uatztjq4bh9/20181217%20Surveys%20simplified%20data%20for%20stackX.xlsx?dl=0
结论与要求：
在我看来，none 这些替代优化方法已经成功；事实上，其中一些人似乎已经提出了其他 warnings/errors 这会让我陷入另一个困境。
任何人都可以告诉我如何在拟合这些模型方面取得进展吗？
我的目的不是让这些成为最终模型，而是挖掘它们，然后 select optimal/top 来自不同替代子集模型的模型。
tl;dr这看起来像是完全分离的情况；在您的 "burned" 条件下，您根本没有任何积极成果。您不必 需要担心这一点 - AIC 比较应该仍然相当稳健 - 但您可能想在继续之前了解发生了什么。此问题（和补救措施）在 GLMM FAQ (and there are a variety of relevant questions/answers on CrossValidated) 的相关部分进行了讨论。
我怎么知道？以下是系数：
(Intercept) s.can_perc s.can_n s.time s.temp
-19.29632 -0.22153 0.45840 0.05241 -0.24990
s.cloud_cover factor(burnt)unburnt s.time:s.temp
-0.19692 19.02091 -0.13949
任何时候（二项式或泊松式）GLM 中的系数（绝对值）大于 8-10，您都必须担心（除非您正在查看以非常大的单位，例如，如果您以十亿吨为单位查看后院的碳量）。这意味着预测变量的一个单位变化会导致对数几率发生（比如说）10 个单位的变化（对于 binomial/logit-link 模型），例如从概率 0.006 (plogis(-5)) 到 0.994 (plogis(5))。在您的情况下，截距为 -19.29，因此在所有预测变量的零值 在燃烧条件 下，您得到的概率为 4.2e-9。另一个巨大的系数是 unburnt (19.02)，因此在未燃烧（未燃烧？）条件下所有预测变量的值为零时，您得到 plogis(-19.29+19.02) = 0.43。
我正在使用 R 中的 lme4 的 glmer 函数分析数据（包括在下面）。
我正在构建的模型由一个泊松分布响应变量（obs）、一个随机因子（area）、一个连续偏移量（duration）、五个连续固定效应（can_perc、can_n、time、temp、cloud_cover) 和一个二项式固定效应因子 (burnt)。
在拟合模型之前，我检查了共线性并删除了所有共线性变量。
初始模型为：
q1 = glmer(obs ~ can_perc + can_n + time * temp +
cloud_cover + factor(burnt) + (1|area) + offset(dat$duration),
data=dat, family=poisson, na.action = na.fail)
（注意：我需要将 na.action 指定为 'na.fail'，因为我想稍后 dredge() 模型，这是必需的。）
运行 模型给出以下警告：
"Hessian is numerically singular: parameters are not uniquely determined"
在模型的类似变体中，我也收到了警告：
"In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: large eigenvalue ratio - Rescale variables?"
根据我对此处 https://rdrr.io/cran/lme4/man/troubleshooting.html 和其他地方建议的有限理解，这两个警告都反映了一个类似的问题，即 Hessian（逆曲率矩阵）具有较大的特征值，表明（在数值公差范围内）表面在某个方向上是完全平坦的。
根据警告和 link 中的建议，我使用 scale() 重新调整了所有连续预测变量。我还缩放了偏移量变量（我尝试了缩放和不缩放这个变量）。带有缩放预测变量的模型在这里：
q2 = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp +
s.cloud_cover + factor(burnt) + (1|area) +
offset(dat$s.duration),
data=dat, family=poisson, na.action = na.fail)
但是我还没有逃过特征值！缩放模型给出了两个警告：
"unable to evaluate scaled gradient"
"Model failed to converge: degenerate Hessian with 1 negative eigenvalues"
我在网上搜索了很多，但找不到另一个 case/solution 来说明如何在预测变量缩放后处理特征值问题，除了检查模型是否没有被错误指定。
尝试解决 warnings/improve 优化：
基于这些 pages/documents： https://cran.r-project.org/web/packages/lme4/lme4.pdf
https://rdrr.io/cran/lme4/man/isSingular.html
https://stats.stackexchange.com/questions/242109/model-failed-to-converge-warning-in-lmer
和其他人，
我有：
检查了模型规格和数据是否有错误（none 我能看到 - 我是不是漏掉了什么？）
使用
is_singular(x, tol = 1e-05)检查奇异性（这个函数调用不知何故从isSingular()演变为当前形式？）：所有模型都给出 FALSE。用
converge_ok(q2, tolerance = 0.001)检查了收敛性措施：所有模型都给出FALSE，除非我大幅增加公差；然而，它们在收敛措施上确实存在很大差异。尝试了不同的optimizers/model估计方法如下：
- a)
glmerControl(optimizer = "bobyqa") and glmerControl(optimizer ="Nelder_Mead") - b)
glmerControl(optimizer ='optimx', optCtrl=list(method='nlminb')) - c) bobyqa、Nelder_Mead、optimx.nlminb、optimx.L-BFGS-B、nloptwrap.NLOPT_LN_NELDERMEAD、nloptwrap.NLOPT_LN_BOBYQA 和 nmkbw 优化器，使用
all_fit()来自 optimx 包的函数。
- a)
代码如下：
# singularity and convergence for first two models:
is_singular(s1, tol = 1e-05) # FALSE (a good thing?)
converge_ok(s1, tol = 1e-05) # FALSE (a bad thing?) 0.0259109730912352
is_singular(s2, tol = 1e-05) # FALSE (a good thing?)
converge_ok(s2, tol = 1e-05) # FALSE (a bad thing?) 0.0023434329028163
# I looked at singularity and converge measures for the others below, but omitted for brevity.
# Alternate optimisations for q1:
q1.bobyqa = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
# Warning 1: unable to evaluate scaled gradient
# Warning 2: Model failed to converge: degenerate Hessian with 1 negative eigenvalues
q1.neldermead = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer ="Nelder_Mead", optCtrl = list(maxfun = 2e5)))
# Warning: unable to evaluate scaled gradient Hessian is numerically singular: parameters are not uniquely determined
q1.nlminb = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer ='optimx', optCtrl=list(method='nlminb')))
# Warning: Parameters or bounds appear to have different scalings. This can cause poor performance in optimization.
# It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.convergence code 9999 from optimxError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, : (maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate
all_fit(q1)
# Alternate optimisations for q2:
q2.bobyqa = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover + factor(burnt) + (1|area) + offset(dat$s.duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
# Warning 1: unable to evaluate scaled gradient
# Warning 2: Model failed to converge: degenerate Hessian with 1 negative eigenvalues
q2.neldermead = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover + factor(burnt) + (1|area) + offset(dat$s.duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer ="Nelder_Mead", optCtrl = list(maxfun = 2e5)))
# Warning: unable to evaluate scaled gradient Hessian is numerically singular: parameters are not uniquely determined
q2.nlminb = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover + factor(burnt) + (1|area) + offset(dat$s.duration), data=dat, family=poisson, na.action = na.fail, control = glmerControl(optimizer ='optimx', optCtrl=list(method='nlminb')))
# Warning: Model is nearly unidentifiable: large eigenvalue ratio - Rescale variables?
all_fit(q2)
以上代码的输出，对于未缩放模型 (q1)：
is_singular(s1, tol = 1e-05) # FALSE (a good thing?)
[1] FALSE
converge_ok(s1, tol = 1e-05) # FALSE (a bad thing?) 0.0259109730912352
0.0259109730912352
FALSE
is_singular(s2, tol = 1e-05) # FALSE (a good thing?)
[1] FALSE
alternate optimisations for original model:
q1.bobyqa = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues
alternate optimisations for original model:
q1.bobyqa = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues
q1.neldermead = glmer(obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1|area) + offset(dat$duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer ="Nelder_Mead", optCtrl = list(maxfun = 2e5)))
unable to evaluate scaled gradient Hessian is numerically singular: parameters are not uniquely determined
all_fit(q1)
bobyqa. : unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues[OK]
Nelder_Mead. : unable to evaluate scaled gradient Hessian is numerically singular: parameters are not uniquely determined[OK]
optimx.nlminb : Parameters or bounds appear to have different scalings.
This can cause poor performance in optimization.
It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.convergence code 9999 from optimxParameters or bounds appear to have different scalings.
This can cause poor performance in optimization.
It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.convergence code 9999 from optimx[ERROR]
optimx.L-BFGS-B : Parameters or bounds appear to have different scalings.
This can cause poor performance in optimization.
It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.convergence code 9999 from optimxParameters or bounds appear to have different scalings.
This can cause poor performance in optimization.
It is important for derivative free methods like BOBYQA, UOBYQA, NEWUOA.convergence code 9999 from optimx[ERROR]
nloptwrap.NLOPT_LN_NELDERMEAD : [ERROR]
nloptwrap.NLOPT_LN_BOBYQA : [ERROR]
nmkbw. : [ERROR]
$`bobyqa.`
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1 | area) + offset(dat$duration)
Data: dat
AIC BIC logLik deviance df.resid
311.0473 330.3356 -146.5237 293.0473 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 1.992
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept) can_perc can_n time temp
-67.4998 -1.3180 0.0239 4.8025 1.7793
cloud_cover factor(burnt)unburnt time:temp
-0.3813 18.5676 -0.1748
convergence code 0; 2 optimizer warnings; 0 lme4 warnings
$Nelder_Mead.
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: obs ~ can_perc + can_n + time * temp + cloud_cover + factor(burnt) + (1 | area) + offset(dat$duration)
Data: dat
AIC BIC logLik deviance df.resid
311.0473 330.3356 -146.5237 293.0473 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 1.992
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept)
can_perc can_n time temp
-67.48057 -1.31791 0.02389 4.80463 1.78012
cloud_cover factor(burnt)unburnt time:temp
-0.38118 18.52637 -0.17483
convergence code 0; 2 optimizer warnings; 0 lme4 warnings
$optimx.nlminb
<std::runtime_error in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): (maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate>
$`optimx.L-BFGS-B`
<std::runtime_error in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): (maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate>
$nloptwrap.NLOPT_LN_NELDERMEAD
<simpleError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): Downdated VtV is not positive definite>
$nloptwrap.NLOPT_LN_BOBYQA
<simpleError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): Downdated VtV is not positive definite>
$nmkbw.
<std::runtime_error in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): (maxstephalfit) PIRLS step-halvings failed to reduce deviance in pwrssUpdate>
上述代码的输出，对于缩放模型 (q2)：
alternate optimisations for q2:
q2.bobyqa = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover + factor(burnt) + (1|area) + offset(dat$s.duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5)))
Model is nearly unidentifiable: large eigenvalue ratio - Rescale variables?
q2.neldermead = glmer(obs ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover + factor(burnt) + (1|area) + offset(dat$s.duration), data=dat, family=poisson, na.action = na.fail, glmerControl(optimizer ="Nelder_Mead", optCtrl = list(maxfun = 2e5)))
unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues
all_fit(q2)
bobyqa. : Model is nearly unidentifiable: large eigenvalue ratio
- Rescale variables?[OK]
Nelder_Mead. : unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues[OK]
optimx.nlminb : Model is nearly unidentifiable: large eigenvalue ratio
- Rescale variables?[OK]
optimx.L-BFGS-B : unable to evaluate scaled gradientModel failed to converge: degenerate Hessian with 1 negative eigenvalues[OK]
nloptwrap.NLOPT_LN_NELDERMEAD : [ERROR]
nloptwrap.NLOPT_LN_BOBYQA : [ERROR]
nmkbw. : [ERROR]
$`bobyqa.`
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: n_shreiberi ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover +
factor(burnt) + (1 | area) + offset(dat$s.duration)
Data: dat
AIC BIC logLik deviance df.resid
316.8412 336.1294 -149.4206 298.8412 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 2.523
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept) s.can_perc s.can_n s.time s.temp
-18.19816 -0.22152 0.45839 0.05239 -0.24983
s.cloud_cover factor(burnt)unburnt s.time:s.temp
-0.19691 17.92390 -0.13948
convergence code 0; 1 optimizer warnings; 0 lme4 warnings
$Nelder_Mead.
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: n_shreiberi ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover +
factor(burnt) + (1 | area) + offset(dat$s.duration)
Data: dat
AIC BIC logLik deviance df.resid
316.8408 336.1290 -149.4204 298.8408 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 2.524
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept) s.can_perc s.can_n s.time s.temp
-19.29632 -0.22153 0.45840 0.05241 -0.24990
s.cloud_cover factor(burnt)unburnt s.time:s.temp
-0.19692 19.02091 -0.13949
convergence code 0; 2 optimizer warnings; 0 lme4 warnings
$optimx.nlminb
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: n_shreiberi ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover +
factor(burnt) + (1 | area) + offset(dat$s.duration)
Data: dat
AIC BIC logLik deviance df.resid
316.8412 336.1294 -149.4206 298.8412 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 2.523
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept) s.can_perc s.can_n s.time s.temp
-18.23626 -0.22152 0.45839 0.05239 -0.24983
s.cloud_cover factor(burnt)unburnt s.time:s.temp
-0.19691 17.96199 -0.13948
convergence code 0; 1 optimizer warnings; 0 lme4 warnings
$`optimx.L-BFGS-B`
Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) ['glmerMod']
Family: poisson ( log )
Formula: n_shreiberi ~ s.can_perc + s.can_n + s.time * s.temp + s.cloud_cover +
factor(burnt) + (1 | area) + offset(dat$s.duration)
Data: dat
AIC BIC logLik deviance df.resid
316.8412 336.1294 -149.4206 298.8412 54
Random effects:
Groups Name Std.Dev.
area (Intercept) 2.524
Number of obs: 63, groups: area, 8
Fixed Effects:
(Intercept) s.can_perc s.can_n s.time s.temp
-18.23581 -0.22155 0.45841 0.05242 -0.24997
s.cloud_cover factor(burnt)unburnt s.time:s.temp
-0.19694 17.96246 -0.13943
convergence code 0; 2 optimizer warnings; 0 lme4 warnings
$nloptwrap.NLOPT_LN_NELDERMEAD
<simpleError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): Downdated VtV is not positive definite>
$nloptwrap.NLOPT_LN_BOBYQA
<simpleError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): Downdated VtV is not positive definite>
$nmkbw.
<simpleError in pwrssUpdate(pp, resp, tol = tolPwrss, GQmat = GQmat, compDev = compDev, grpFac = fac, maxit = maxit, verbose = verbose): Downdated VtV is not positive definite>
数据：
数据集可在此处获得link： https://www.dropbox.com/s/ud50uatztjq4bh9/20181217%20Surveys%20simplified%20data%20for%20stackX.xlsx?dl=0
结论与要求：
在我看来，none 这些替代优化方法已经成功；事实上，其中一些人似乎已经提出了其他 warnings/errors 这会让我陷入另一个困境。
任何人都可以告诉我如何在拟合这些模型方面取得进展吗？ 我的目的不是让这些成为最终模型，而是挖掘它们，然后 select optimal/top 来自不同替代子集模型的模型。
tl;dr这看起来像是完全分离的情况；在您的 "burned" 条件下，您根本没有任何积极成果。您不必 需要担心这一点 - AIC 比较应该仍然相当稳健 - 但您可能想在继续之前了解发生了什么。此问题（和补救措施）在 GLMM FAQ (and there are a variety of relevant questions/answers on CrossValidated) 的相关部分进行了讨论。
我怎么知道？以下是系数：
(Intercept) s.can_perc s.can_n s.time s.temp
-19.29632 -0.22153 0.45840 0.05241 -0.24990
s.cloud_cover factor(burnt)unburnt s.time:s.temp
-0.19692 19.02091 -0.13949
任何时候（二项式或泊松式）GLM 中的系数（绝对值）大于 8-10，您都必须担心（除非您正在查看以非常大的单位，例如，如果您以十亿吨为单位查看后院的碳量）。这意味着预测变量的一个单位变化会导致对数几率发生（比如说）10 个单位的变化（对于 binomial/logit-link 模型），例如从概率 0.006 (plogis(-5)) 到 0.994 (plogis(5))。在您的情况下，截距为 -19.29，因此在所有预测变量的零值 在燃烧条件 下，您得到的概率为 4.2e-9。另一个巨大的系数是 unburnt (19.02)，因此在未燃烧（未燃烧？）条件下所有预测变量的值为零时，您得到 plogis(-19.29+19.02) = 0.43。