Calling libraries
library(lme4)
## Loading required package: Matrix
Tidy Data
path = "~/201 2025/Hibernation_Data.csv"
hdf <-read.csv(path)
hdf$Sex <- as.factor(hdf$Sex)
Linear Mixed Model modeling Mass
lm1 <- lmer(Mass ~ Sex + ExpWk + Sex:ExpWk + FoodInt + PercFat + BMI + (1 | AnNum), data = hdf)
summary(lm1)
## Linear mixed model fit by REML ['lmerMod']
## Formula: Mass ~ Sex + ExpWk + Sex:ExpWk + FoodInt + PercFat + BMI + (1 |
## AnNum)
## Data: hdf
##
## REML criterion at convergence: 41.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.78656 -0.25228 0.01139 0.22002 0.76378
##
## Random effects:
## Groups Name Variance Std.Dev.
## AnNum (Intercept) 127.905 11.309
## Residual 4.735 2.176
## Number of obs: 14, groups: AnNum, 5
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -14.21752 89.42624 -0.159
## SexM 11.90993 13.92528 0.855
## ExpWkPstHib3 9.32994 14.81035 0.630
## ExpWkPstHib4 13.31567 9.65295 1.379
## FoodInt -1.55807 1.97308 -0.790
## PercFat -0.01129 0.35656 -0.032
## BMI 36.90287 19.44914 1.897
## SexM:ExpWkPstHib3 -2.58632 17.17902 -0.151
## SexM:ExpWkPstHib4 -4.98426 13.53549 -0.368
##
## Correlation of Fixed Effects:
## (Intr) SexM ExWPH3 ExWPH4 FodInt PercFt BMI SM:EWPH3
## SexM -0.655
## ExpWkPstHb3 -0.959 0.640
## ExpWkPstHb4 -0.953 0.625 0.965
## FoodInt 0.740 -0.617 -0.830 -0.769
## PercFat 0.862 -0.513 -0.855 -0.900 0.556
## BMI -0.995 0.616 0.970 0.962 -0.771 -0.873
## SxM:ExpWPH3 0.968 -0.634 -0.992 -0.966 0.792 0.872 -0.976
## SxM:ExpWPH4 0.973 -0.623 -0.962 -0.982 0.750 0.872 -0.977 0.973
Linear Mixed Model modeling BMI
lm2 <- lmer(BMI ~ Sex + ExpWk + Sex:ExpWk + FoodInt + PercFat + Mass + (1 | AnNum), data = hdf)
summary(lm2)
## Linear mixed model fit by REML ['lmerMod']
## Formula: BMI ~ Sex + ExpWk + Sex:ExpWk + FoodInt + PercFat + Mass + (1 |
## AnNum)
## Data: hdf
##
## REML criterion at convergence: 6.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.10874 -0.23986 0.01941 0.31823 1.06314
##
## Random effects:
## Groups Name Variance Std.Dev.
## AnNum (Intercept) 0.002176 0.04664
## Residual 0.002351 0.04849
## Number of obs: 14, groups: AnNum, 5
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.402173 0.391101 8.699
## SexM -0.355120 0.076430 -4.646
## ExpWkPstHib3 -0.550536 0.099110 -5.555
## ExpWkPstHib4 -0.437298 0.063425 -6.895
## FoodInt 0.046837 0.015244 3.072
## PercFat 0.012603 0.004308 2.925
## Mass 0.007958 0.002776 2.867
## SexM:ExpWkPstHib3 0.598446 0.127701 4.686
## SexM:ExpWkPstHib4 0.521664 0.088586 5.889
##
## Correlation of Fixed Effects:
## (Intr) SexM ExWPH3 ExWPH4 FodInt PercFt Mass SM:EWPH3
## SexM -0.411
## ExpWkPstHb3 -0.696 0.559
## ExpWkPstHb4 -0.459 0.541 0.637
## FoodInt 0.478 -0.577 -0.594 -0.387
## PercFat 0.660 -0.363 -0.650 -0.625 0.400
## Mass -0.979 0.405 0.725 0.484 -0.582 -0.749
## SxM:ExpWPH3 0.771 -0.583 -0.933 -0.605 0.544 0.693 -0.794
## SxM:ExpWPH4 0.704 -0.589 -0.662 -0.802 0.415 0.595 -0.699 0.746
Linear Mixed Model modeling FoodInt
lm3 <- lmer(FoodInt ~ ExpWk + Sex:ExpWk + PercFat + Mass + BMI + (1 | AnNum), data = hdf)
summary(lm3)
## Linear mixed model fit by REML ['lmerMod']
## Formula: FoodInt ~ ExpWk + Sex:ExpWk + PercFat + Mass + BMI + (1 | AnNum)
## Data: hdf
##
## REML criterion at convergence: 28.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.64018 -0.48002 0.02578 0.31839 0.87512
##
## Random effects:
## Groups Name Variance Std.Dev.
## AnNum (Intercept) 2.2297 1.4932
## Residual 0.3217 0.5671
## Number of obs: 14, groups: AnNum, 5
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -37.74806 13.42938 -2.811
## ExpWkPstHib3 7.06798 1.94882 3.627
## ExpWkPstHib4 4.86036 1.68397 2.886
## PercFat -0.12596 0.07011 -1.797
## Mass -0.05749 0.07544 -0.762
## BMI 10.39137 3.89634 2.667
## ExpWkPstHib2:SexM 5.00244 1.71794 2.912
## ExpWkPstHib3:SexM -2.52690 2.24932 -1.123
## ExpWkPstHib4:SexM -0.91766 1.91258 -0.480
##
## Correlation of Fixed Effects:
## (Intr) ExWPH3 ExWPH4 PercFt Mass BMI EWPH2: EWPH3:
## ExpWkPstHb3 -0.899
## ExpWkPstHb4 -0.792 0.862
## PercFat 0.779 -0.799 -0.733
## Mass 0.097 -0.223 -0.524 -0.012
## BMI -0.773 0.788 0.903 -0.573 -0.702
## ExpWkPH2:SM -0.483 0.490 0.550 -0.368 -0.334 0.521
## ExpWkPH3:SM 0.607 -0.644 -0.391 0.601 -0.259 -0.302 0.288
## ExpWkPH4:SM 0.572 -0.533 -0.459 0.521 -0.130 -0.360 0.353 0.896
Linear Mixed Model modeling PercFat
lm4 <- lmer(PercFat ~ ExpWk + Sex:ExpWk + Mass + BMI + FoodInt + (1 | AnNum), data = hdf)
summary(lm3)
## Linear mixed model fit by REML ['lmerMod']
## Formula: FoodInt ~ ExpWk + Sex:ExpWk + PercFat + Mass + BMI + (1 | AnNum)
## Data: hdf
##
## REML criterion at convergence: 28.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.64018 -0.48002 0.02578 0.31839 0.87512
##
## Random effects:
## Groups Name Variance Std.Dev.
## AnNum (Intercept) 2.2297 1.4932
## Residual 0.3217 0.5671
## Number of obs: 14, groups: AnNum, 5
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -37.74806 13.42938 -2.811
## ExpWkPstHib3 7.06798 1.94882 3.627
## ExpWkPstHib4 4.86036 1.68397 2.886
## PercFat -0.12596 0.07011 -1.797
## Mass -0.05749 0.07544 -0.762
## BMI 10.39137 3.89634 2.667
## ExpWkPstHib2:SexM 5.00244 1.71794 2.912
## ExpWkPstHib3:SexM -2.52690 2.24932 -1.123
## ExpWkPstHib4:SexM -0.91766 1.91258 -0.480
##
## Correlation of Fixed Effects:
## (Intr) ExWPH3 ExWPH4 PercFt Mass BMI EWPH2: EWPH3:
## ExpWkPstHb3 -0.899
## ExpWkPstHb4 -0.792 0.862
## PercFat 0.779 -0.799 -0.733
## Mass 0.097 -0.223 -0.524 -0.012
## BMI -0.773 0.788 0.903 -0.573 -0.702
## ExpWkPH2:SM -0.483 0.490 0.550 -0.368 -0.334 0.521
## ExpWkPH3:SM 0.607 -0.644 -0.391 0.601 -0.259 -0.302 0.288
## ExpWkPH4:SM 0.572 -0.533 -0.459 0.521 -0.130 -0.360 0.353 0.896
jtools::summ(lm1)
|
Observations
|
14
|
|
Dependent variable
|
Mass
|
|
Type
|
Mixed effects linear regression
|
|
AIC
|
63.39
|
|
BIC
|
70.42
|
|
Pseudo-R² (fixed effects)
|
0.54
|
|
Pseudo-R² (total)
|
0.98
|
|
Fixed Effects
|
|
|
Est.
|
S.E.
|
t val.
|
d.f.
|
p
|
|
(Intercept)
|
-14.22
|
89.43
|
-0.16
|
2.66
|
0.88
|
|
SexM
|
11.91
|
13.93
|
0.86
|
4.81
|
0.43
|
|
ExpWkPstHib3
|
9.33
|
14.81
|
0.63
|
2.61
|
0.58
|
|
ExpWkPstHib4
|
13.32
|
9.65
|
1.38
|
2.50
|
0.28
|
|
FoodInt
|
-1.56
|
1.97
|
-0.79
|
3.10
|
0.49
|
|
PercFat
|
-0.01
|
0.36
|
-0.03
|
2.26
|
0.98
|
|
BMI
|
36.90
|
19.45
|
1.90
|
2.61
|
0.17
|
|
SexM:ExpWkPstHib3
|
-2.59
|
17.18
|
-0.15
|
2.58
|
0.89
|
|
SexM:ExpWkPstHib4
|
-4.98
|
13.54
|
-0.37
|
2.56
|
0.74
|
|
p values calculated using Satterthwaite d.f.
|
|
Random Effects
|
|
Group
|
Parameter
|
Std. Dev.
|
|
AnNum
|
(Intercept)
|
11.31
|
|
Residual
|
|
2.18
|
|
Grouping Variables
|
|
Group
|
# groups
|
ICC
|
|
AnNum
|
5
|
0.96
|
jtools::summ(lm2)
|
Observations
|
14
|
|
Dependent variable
|
BMI
|
|
Type
|
Mixed effects linear regression
|
|
AIC
|
28.43
|
|
BIC
|
35.46
|
|
Pseudo-R² (fixed effects)
|
0.95
|
|
Pseudo-R² (total)
|
0.98
|
|
Fixed Effects
|
|
|
Est.
|
S.E.
|
t val.
|
d.f.
|
p
|
|
(Intercept)
|
3.40
|
0.39
|
8.70
|
1.76
|
0.02
|
|
SexM
|
-0.36
|
0.08
|
-4.65
|
2.65
|
0.02
|
|
ExpWkPstHib3
|
-0.55
|
0.10
|
-5.55
|
4.98
|
0.00
|
|
ExpWkPstHib4
|
-0.44
|
0.06
|
-6.89
|
3.81
|
0.00
|
|
FoodInt
|
0.05
|
0.02
|
3.07
|
2.41
|
0.07
|
|
PercFat
|
0.01
|
0.00
|
2.93
|
4.41
|
0.04
|
|
Mass
|
0.01
|
0.00
|
2.87
|
2.52
|
0.08
|
|
SexM:ExpWkPstHib3
|
0.60
|
0.13
|
4.69
|
4.97
|
0.01
|
|
SexM:ExpWkPstHib4
|
0.52
|
0.09
|
5.89
|
5.00
|
0.00
|
|
p values calculated using Satterthwaite d.f.
|
|
Random Effects
|
|
Group
|
Parameter
|
Std. Dev.
|
|
AnNum
|
(Intercept)
|
0.05
|
|
Residual
|
|
0.05
|
|
Grouping Variables
|
|
Group
|
# groups
|
ICC
|
|
AnNum
|
5
|
0.48
|
jtools::summ(lm3)
|
Observations
|
14
|
|
Dependent variable
|
FoodInt
|
|
Type
|
Mixed effects linear regression
|
|
AIC
|
50.20
|
|
BIC
|
57.23
|
|
Pseudo-R² (fixed effects)
|
0.55
|
|
Pseudo-R² (total)
|
0.94
|
|
Fixed Effects
|
|
|
Est.
|
S.E.
|
t val.
|
d.f.
|
p
|
|
(Intercept)
|
-37.75
|
13.43
|
-2.81
|
4.83
|
0.04
|
|
ExpWkPstHib3
|
7.07
|
1.95
|
3.63
|
4.19
|
0.02
|
|
ExpWkPstHib4
|
4.86
|
1.68
|
2.89
|
3.93
|
0.05
|
|
PercFat
|
-0.13
|
0.07
|
-1.80
|
4.38
|
0.14
|
|
Mass
|
-0.06
|
0.08
|
-0.76
|
4.07
|
0.49
|
|
BMI
|
10.39
|
3.90
|
2.67
|
3.99
|
0.06
|
|
ExpWkPstHib2:SexM
|
5.00
|
1.72
|
2.91
|
3.15
|
0.06
|
|
ExpWkPstHib3:SexM
|
-2.53
|
2.25
|
-1.12
|
3.40
|
0.33
|
|
ExpWkPstHib4:SexM
|
-0.92
|
1.91
|
-0.48
|
3.00
|
0.66
|
|
p values calculated using Satterthwaite d.f.
|
|
Random Effects
|
|
Group
|
Parameter
|
Std. Dev.
|
|
AnNum
|
(Intercept)
|
1.49
|
|
Residual
|
|
0.57
|
|
Grouping Variables
|
|
Group
|
# groups
|
ICC
|
|
AnNum
|
5
|
0.87
|
jtools::summ(lm4)
|
Observations
|
14
|
|
Dependent variable
|
PercFat
|
|
Type
|
Mixed effects linear regression
|
|
AIC
|
61.50
|
|
BIC
|
68.53
|
|
Pseudo-R² (fixed effects)
|
0.80
|
|
Pseudo-R² (total)
|
0.86
|
|
Fixed Effects
|
|
|
Est.
|
S.E.
|
t val.
|
d.f.
|
p
|
|
(Intercept)
|
-185.77
|
48.89
|
-3.80
|
4.99
|
0.01
|
|
ExpWkPstHib3
|
31.84
|
7.55
|
4.22
|
4.54
|
0.01
|
|
ExpWkPstHib4
|
24.72
|
6.32
|
3.91
|
4.96
|
0.01
|
|
Mass
|
-0.21
|
0.25
|
-0.81
|
4.31
|
0.46
|
|
BMI
|
48.27
|
17.14
|
2.82
|
4.97
|
0.04
|
|
FoodInt
|
-2.80
|
0.84
|
-3.32
|
0.98
|
0.19
|
|
ExpWkPstHib2:SexM
|
19.64
|
5.96
|
3.29
|
3.13
|
0.04
|
|
ExpWkPstHib3:SexM
|
-16.57
|
4.95
|
-3.35
|
2.77
|
0.05
|
|
ExpWkPstHib4:SexM
|
-10.12
|
4.36
|
-2.32
|
3.00
|
0.10
|
|
p values calculated using Satterthwaite d.f.
|
|
Random Effects
|
|
Group
|
Parameter
|
Std. Dev.
|
|
AnNum
|
(Intercept)
|
2.02
|
|
Residual
|
|
3.19
|
|
Grouping Variables
|
|
Group
|
# groups
|
ICC
|
|
AnNum
|
5
|
0.29
|