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我的混合效果 model 公式在 R 中是否不正確？

[英]Is my mixed effect model formula incorrect in R?

 原文  2022-09-09 14:41:30  1   1    r/ mixed-model

問題描述

我正在做一項研究，我想分析具有混合效應 model 的數據。 我有三個固定效果和一個隨機效果。 我的代碼 output 似乎有點不對勁，我不確定這是代碼的結構問題，還是我的數據中的多重共線性問題。 我嘗試過測試 fpr 共線性，但還沒有讓代碼工作（我想是因為我主要有分類數據）

Fixed Effects:
soil_type - 2 groups ("Medium" and "Fine")
treatment - 4 groups ("L", "S", "K", "C")
days - 3 sampling points (day 4, 11, 18)

Random Effect:
replicates - 3 groups (1,2,3)

我的代碼如下：

cl.mod <- lmer(weighted_cl ~ soil_type + treatment + days + (1|rep),
               data = leach.conc, REML = FALSE)

我相信我有正確的代碼，但是當我查看 output 時，我不確定我是否缺少值：

Fixed effects:
                Estimate Std. Error t value
(Intercept)      7.01992    1.65258   4.248
soil_typeMedium -4.81518    1.05431  -4.567
treatmentKCl    10.48391    1.49103   7.031
treatmentLiquid 25.25578    1.49103  16.939
treatmentSolid   8.31138    1.49103   5.574
days            -0.32534    0.09223  -3.527

Correlation of Fixed Effects:
            (Intr) sl_tyM trtmKC trtmnL trtmnS
soil_typMdm -0.319                            
treatmntKCl -0.451  0.000                     
treatmntLqd -0.451  0.000  0.500              
treatmntSld -0.451  0.000  0.500  0.500       
days        -0.614  0.000  0.000  0.000  0.000*

我不確定這是否是因為我的數據存在多重共線性，或者我的代碼不正確（或兩者兼而有之）。 因為這是分類數據，所以我不確定是否要測試共線性。 此外，我的數據中沒有缺失值。 任何指導或看的東西將不勝感激！

1 個解決方案

解決方案1
 0  2022-09-13 05:50:37

數據

因此，您的問題中有很多問題，並且鑒於您的數據不在手邊，我將使用我自己的玩具數據集來回答您的問題。 首先，如果您想檢查自己，請dput我的數據：

work <- structure(list(Work_Environment = c("Office", "Office", "Office", 
"Home", "Home", "Office", "Office", "Office", "Office", "Office", 
"Home", "Home", "Office", "Office", "Office", "Home", "Office", 
"Home", "Home", "Office", "Office", "Home", "Office", "Home", 
"Home", "Home", "Office", "Office", "Office", "Office", "Home", 
"Home", "Home", "Office", "Office", "Office", "Office", "Office", 
"Home", "Home", "Office", "Office", "Home", "Home", "Office", 
"Home", "Home", "Office", "Office", "Home", "Home", "Office", 
"Home", "Home", "Office", "Office", "Home", "Office", "Home", 
"Home", "Home", "Home", "Office", "Home", "Office", "Office", 
"Home", "Home", "Office", "Office", "Home", "Home", "Office", 
"Office", "Home", "Office", "Office", "Home", "Office", "Office", 
"Home", "Home", "Office", "Office", "Home", "Home", "Office", 
"Home", "Home", "Office", "Office", "Home", "Office", "Office", 
"Home", "Home", "Office", "Home", "Home", "Home", "Home", "Home", 
"Home", "Office", "Home", "Office", "Office", "Home", "Home", 
"Home", "Office", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Office", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Office", "Home", "Office", "Home", "Office", 
"Office", "Office", "Office", "Home", "Home", "Home", "Home", 
"Office", "Home", "Office", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Office", "Office", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Office", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Office", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Office", "Office", "Office", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Office", "Office", "Home", "Home", 
"Office", "Office", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Home", "Home", "Home", 
"Home", "Home", "Home", "Home", "Home", "Office", "Office", "Office", 
"Home", "Office", "Home", "Home", "Home", "Home"), Coffee_Cups = c(3L, 
0L, 2L, 6L, 4L, 5L, 3L, 3L, 2L, 2L, 3L, 1L, 1L, 3L, 2L, 2L, 0L, 
1L, 1L, 4L, 4L, 3L, 0L, 1L, 3L, 0L, 0L, 0L, 0L, 2L, 0L, 1L, 2L, 
3L, 2L, 2L, 4L, 3L, 6L, 6L, 3L, 4L, 6L, 8L, 3L, 5L, 0L, 2L, 2L, 
8L, 6L, 4L, 6L, 4L, 4L, 2L, 6L, 6L, 5L, 1L, 3L, 1L, 5L, 4L, 6L, 
5L, 0L, 6L, 6L, 4L, 4L, 2L, 2L, 6L, 6L, 7L, 3L, 3L, 0L, 5L, 7L, 
6L, 3L, 5L, 3L, 3L, 1L, 9L, 9L, 3L, 3L, 6L, 6L, 6L, 3L, 0L, 7L, 
6L, 6L, 3L, 9L, 3L, 8L, 8L, 3L, 3L, 7L, 6L, 3L, 3L, 3L, 6L, 6L, 
6L, 1L, 9L, 3L, 3L, 2L, 6L, 3L, 6L, 9L, 6L, 8L, 9L, 6L, 6L, 6L, 
0L, 3L, 0L, 3L, 3L, 6L, 3L, 0L, 9L, 3L, 0L, 2L, 0L, 6L, 6L, 6L, 
3L, 6L, 3L, 9L, 3L, 0L, 0L, 6L, 3L, 3L, 3L, 3L, 6L, 0L, 6L, 3L, 
3L, 5L, 5L, 3L, 0L, 6L, 4L, 2L, 0L, 2L, 4L, 0L, 6L, 4L, 4L, 2L, 
2L, 0L, 9L, 6L, 3L, 6L, 6L, 9L, 0L, 6L, 6L, 6L, 6L, 6L, 6L, 3L, 
3L, 0L, 9L, 6L, 3L, 6L, 3L, 6L, 1L, 6L, 6L, 6L, 6L, 6L, 1L, 3L, 
9L, 6L, 3L, 6L, 9L, 3L, 5L, 6L, 3L, 0L, 6L, 3L, 3L, 5L, 0L, 6L, 
3L, 5L, 3L, 0L, 6L, 7L, 3L, 6L, 6L, 6L, 6L, 3L, 5L, 6L, 7L, 6L, 
6L, 4L, 6L, 4L, 5L, 5L, 6L, NA, 8L, 6L, 6L, 6L, 9L, 3L, 3L, 9L, 
7L, 8L, 4L, 3L, 3L, 3L, 6L, 6L, 6L, 3L, 4L, 3L, 3L, 6L, 4L, 3L, 
3L, 4L, 6L, 0L, 3L, 6L, 4L, 3L, 3L, 7L, 4L, 4L, 3L, 1L, 6L, 4L, 
6L, 5L, 3L, 6L, 6L, 3L, 6L, 3L, 5L, 6L, 6L, 3L, 6L, 4L, 9L, 7L, 
6L, 3L, 3L, 3L, 4L, 6L, 3L, 6L, 3L, 4L, 4L, 3L, 5L, 5L, 5L, 0L, 
6L, 4L, 5L, 6L, 4L, 1L, 6L, 3L, 6L, 6L, 2L, 5L, 5L, 6L, 5L, 4L, 
5L, 4L, 6L, 5L, 0L, 3L, 4L, 4L, 1L, 4L, 3L, 5L, 8L, 1L, 4L, 4L, 
2L, 2L, 3L, 3L, 5L, 3L, 4L, 3L, 3L, 3L, 3L, 3L, 2L, 1L, 4L, 3L, 
5L, 4L, 7L, 5L, 2L, 4L, 1L, 5L, 3L), Time_Wake = c(500L, 715L, 
600L, 600L, 700L, 600L, 700L, 500L, 500L, 500L, 500L, 700L, 645L, 
700L, 630L, 645L, 700L, 600L, 700L, 550L, 700L, 730L, 725L, 800L, 
600L, 640L, 600L, 730L, 650L, 830L, 630L, 630L, 830L, 722L, 641L, 
800L, 720L, 700L, NA, NA, NA, 700L, 700L, 622L, 710L, 632L, 400L, 
640L, 700L, 730L, 830L, 659L, 800L, 701L, 700L, 900L, 930L, 650L, 
930L, NA, 700L, 300L, 830L, 800L, 705L, 647L, 800L, NA, 830L, 
NA, 830L, 838L, 650L, 849L, 500L, 830L, 800L, 321L, 700L, 400L, 
400L, NA, 700L, 600L, 604L, 700L, 730L, 700L, 700L, 500L, 700L, 
630L, 500L, 600L, 700L, 600L, 830L, 600L, 500L, 600L, 738L, 758L, 
645L, 702L, NA, 500L, 849L, 656L, 831L, 700L, 700L, 805L, 834L, 
849L, 407L, 739L, NA, 717L, 852L, 826L, 446L, 919L, 842L, 754L, 
900L, NA, 845L, 900L, 848L, 757L, 927L, 500L, 700L, 430L, 430L, 
NA, 600L, NA, 452L, 700L, NA, 300L, 600L, 600L, 400L, 945L, 500L, 
700L, 700L, 700L, 504L, 700L, 700L, 400L, 747L, NA, 200L, 740L, 
441L, 833L, 815L, 400L, 600L, 600L, 700L, 344L, NA, 636L, 600L, 
NA, 300L, 600L, 600L, 700L, NA, 822L, 360L, 600L, 945L, NA, 656L, 
400L, 700L, 744L, 710L, 600L, NA, 700L, 700L, 700L, 253L, 600L, 
819L, 700L, 600L, 655L, 835L, 848L, 654L, 630L, 745L, 300L, 730L, 
700L, 700L, 700L, 700L, NA, 200L, 700L, 500L, NA, 500L, 700L, 
700L, 730L, 700L, 830L, 825L, 700L, 600L, 700L, 700L, NA, 700L, 
700L, 700L, 700L, 700L, 700L, 300L, 500L, 700L, 705L, NA, 700L, 
723L, 531L, 841L, 845L, 744L, 742L, 830L, 648L, NA, 630L, 645L, 
634L, 727L, 603L, 648L, 721L, 647L, 842L, 750L, 650L, NA, 645L, 
645L, 751L, 130L, 729L, NA, 830L, 730L, 727L, 709L, 641L, NA, 
709L, 710L, 621L, 747L, 720L, 628L, 654L, NA, 633L, 548L, 428L, 
700L, 733L, 700L, 556L, 757L, 815L, 735L, NA, 500L, 707L, 751L, 
601L, 500L, NA, NA, 600L, 800L, 607L, 557L, 723L, 718L, 630L, 
400L, 633L, 550L, 607L, 621L, 640L, 636L, 559L, 417L, 701L, 100L, 
640L, 629L, 614L, 545L, 615L, 550L, 755L, NA, 737L, 725L, 613L, 
713L, 555L, 746L, 634L, 651L, 701L, NA, NA, 810L, 646L, 442L, 
NA, 641L, 642L, 700L, 525L, 332L, 743L, 703L, 718L, 625L, NA, 
618L, NA, NA, 400L, 329L, 748L, 700L, 720L, 602L, 727L, 842L, 
842L, 400L, NA, 704L, 808L, 632L, 746L, 405L, NA, 559L, 649L, 
639L, 709L, 720L, 349L, 650L, 630L, NA, NA, 630L, NA), Mins_Work = c(435L, 
350L, 145L, 135L, 15L, 60L, 60L, 390L, 395L, 395L, 315L, 80L, 
580L, 175L, 545L, 230L, 435L, 370L, 255L, 515L, 330L, 65L, 115L, 
550L, 420L, 45L, 266L, 196L, 198L, 220L, 17L, 382L, 0L, 180L, 
343L, 207L, 263L, 332L, 0L, 0L, 259L, 417L, 282L, 685L, 517L, 
111L, 64L, 466L, 499L, 460L, 269L, 300L, 427L, 301L, 436L, 342L, 
229L, 379L, 102L, 146L, NA, 94L, 345L, 73L, 204L, 512L, 113L, 
135L, 458L, 493L, 552L, 108L, 335L, 395L, 508L, 546L, 396L, 159L, 
325L, 747L, 650L, 377L, 461L, 669L, 186L, 220L, 410L, 708L, 409L, 
515L, 413L, 166L, 451L, 660L, 177L, 192L, 191L, 461L, 637L, 297L, 
601L, 586L, 270L, 479L, 0L, 480L, 397L, 174L, 111L, 0L, 610L, 
332L, 345L, 423L, 160L, 611L, 0L, 345L, 550L, 324L, 427L, 505L, 
632L, 560L, 230L, 495L, 235L, 522L, 654L, 465L, 377L, 260L, 572L, 
612L, 594L, 624L, 237L, 0L, 38L, 409L, 634L, 292L, 706L, 399L, 
568L, 0L, 694L, 298L, 616L, 553L, 581L, 423L, 636L, 623L, 338L, 
345L, 521L, 438L, 504L, 600L, 616L, 656L, 285L, 474L, 688L, 278L, 
383L, 535L, 363L, 470L, 457L, 303L, 123L, 363L, 329L, 513L, 636L, 
421L, 220L, 430L, 428L, 536L, 156L, 615L, 429L, 103L, 332L, 250L, 
281L, 248L, 435L, 589L, 515L, 158L, 0L, 649L, 427L, 193L, 225L, 
0L, 280L, 163L, 536L, 301L, 406L, 230L, 519L, 0L, 303L, 472L, 
392L, 326L, 368L, 405L, 515L, 308L, 259L, 769L, 93L, 517L, 261L, 
420L, 248L, 265L, 834L, 313L, 131L, 298L, 134L, 385L, 648L, 529L, 
487L, 533L, 641L, 429L, 339L, 508L, 560L, 439L, 381L, 397L, 692L, 
534L, 148L, 366L, 167L, 425L, 315L, 476L, 384L, 498L, 502L, 308L, 
360L, 203L, 410L, 626L, 593L, 409L, 531L, 157L, 0L, 357L, 443L, 
615L, 564L, 341L, 352L, 609L, 686L, 386L, 323L, 362L, 597L, 325L, 
51L, 570L, 579L, 284L, 0L, 530L, 171L, 640L, 263L, 112L, 217L, 
152L, 203L, 394L, 135L, 234L, 507L, 224L, 174L, 210L, 138L, 52L, 
326L, 413L, 695L, 370L, 256L, 327L, 490L, 128L, 469L, 567L, 359L, 
561L, 478L, 233L, 550L, 390L, 406L, 56L, 47L, 258L, 332L, 114L, 
193L, 435L, 493L, 659L, 93L, 86L, 0L, 228L, 232L, 318L, 295L, 
639L, 367L, 313L, 253L, 433L, 399L, 269L, 446L, 407L, 424L, 410L, 
309L, 364L, 700L, 345L, 274L, 113L, 202L, 553L, 157L, 351L, 303L, 
392L, 539L, 337L, 297L, 479L, 311L, 173L, 94L, 170L, 469L, 180L, 
311L, 106L, 521L, 378L, 61L, 462L, 644L, 310L, 533L, 517L, 136L, 
0L, 392L, NA)), class = "data.frame", row.names = c(NA, -378L
))

我的 model 中的數據包含兩個預測變量： Coffee_Cups ，即當天喝了多少咖啡杯； Time_Wake ，即當天起床的時間。 此處的Work_Environment被選為具有兩個級別的隨機效果來模擬您所做的事情，但在下面我表示這不是一個明智的選擇。 此 model 中的預期結果或 y 是Mins_Work ，即當天記錄的生產力分鍾數。 您可以使用以下代碼查看數據的結構：

work %>% 
  select(Work_Environment,
         Coffee_Cups,
         Time_Wake,
         Mins_Work) %>%
  glimpse()

如此處所示：

Rows: 378
Columns: 4
$ Work_Environment <chr> "Office", "Office", "Office", "Home", "Home", … $ Coffee_Cups      <int> 3, 0, 2, 6, 4, 5, 3, 3, 2, 2, 3, 1, 1, 3, 2, 2…
$ Time_Wake <int> 500, 715, 600, 600, 700, 600, 700, 500, 500, 5… $ Mins_Work        <int> 435, 350, 145, 135, 15, 60, 60, 390, 395, 395,…

觀察缺失值

目前尚不清楚您的數據中是否缺少值，因為您的lmer摘要中的摘要 output 似乎沒有說明有多少觀察值的部分。 也就是說，您可以在 R 中相當輕松地檢查您丟失的數據。 我在這里檢查了我的兩個固定效應預測器：

#### Check NA Values ###
work %>% 
  select(Mins_Work) %>% 
  is.na() %>% 
  table() # 2 NA values

work %>% 
  select(Time_Wake) %>% 
  is.na() %>% 
  table() # 43 NA values

然后我檢查了我的數據中的總觀察值。

nrow(work) # 378 observations

由於只有 378 個觀測值和 45 個缺失值，我們應該有 333 個由lmer model 觀測到的值。 在這里，我在下面構建了我的lmer model：

hlm.work <- lmer(Mins_Work
                 ~ Coffee_Cups
                 + Time_Wake
                 + (1|Work_Environment),
                 data = work)
summary(hlm.work)

可以看出，model 只保留了 output 中“隨機效應”部分的 333 個觀察值：

Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Mins_Work ~ Coffee_Cups + Time_Wake + (1 | Work_Environment)
   Data: work

REML criterion at convergence: 4338.3

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.51991 -0.70343 -0.01399  0.73630  2.93450 

Random effects:
 Groups           Name        Variance Std.Dev.
 Work_Environment (Intercept)  4289     65.49  
 Residual                     27230    165.01  
Number of obs: 333, groups:  Work_Environment, 2

Fixed effects:
             Estimate Std. Error        df t value Pr(>|t|)    
(Intercept) 400.69391   64.43207   3.34404   6.219  0.00604 ** 
Coffee_Cups  28.71402    4.14095 329.56783   6.934 2.16e-11 ***
Time_Wake    -0.18917    0.06431 329.14364  -2.942  0.00350 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) Cff_Cp
Coffee_Cups -0.172       
Time_Wake   -0.626 -0.124

多重共線性

model 中的 VIF 可以通過performance package 快速觀察。 代碼如下：

library(performance)
check_collinearity(hlm.work)

這表明我們的 VIF 還不足以引起關注：

# Check for Multicollinearity

Low Correlation

        Term  VIF    VIF 95% CI Increased SE Tolerance Tolerance 95% CI
 Coffee_Cups 1.02 [1.00, 17.58]         1.01      0.98     [0.06, 1.00]
   Time_Wake 1.02 [1.00, 17.58]         1.01      0.98     [0.06, 1.00]

Model的適用性

至於您關於 model 的適用性的問題，我所看到的沒有任何錯誤，但正如其他一些人所指出的，您的隨機效應可能太少，無法保證將它們包含在此 model 中。 您可能需要考慮固定效應回歸，或者如果您認為其他隨機效應會導致具有足夠水平的“噪聲”，則可以將它們包括在內。

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