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I tried using a linear mixed-effect model: ""M5 <- lmer(PhiPS2~habitat*sampling_no + (1+ species|habitat), REML=F, data =physio2)"" ""summary(M5) Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: PhiPS2 ~ habitat * sampling_no + (1 + species | habitat) Data: physio2M5 <- lmer(PhiPS2~habitat*sampling_no + (1+ species|habitat), REML=F, data =physio2)

Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: PhiPS2 ~ habitat * sampling_no + (1 + species | habitat)
   Data: physio2

     AIC      BIC   logLik deviance df.resid 
 -1338.5  -1058.2    744.2  -1488.5      235 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0414 -0.5610 -0.0908  0.5200  3.2800 

Random effects:
 Groups   Name                              Variance  Std.Dev.  Corr                                                 
 habitat  (Intercept)                       0.000e+00 0.000e+00                                                      
          speciesArtemesia brevifolia       1.136e-03 3.371e-02   NaN                                                
          speciesAster flaccidus            9.169e-04 3.028e-02   NaN  1.00                                          
          speciesLactuca tatarica           2.085e-12 1.444e-06   NaN -0.62 -0.62                                    
          speciesLeontopodium ochroleucum   3.035e-03 5.509e-02   NaN  1.00  1.00 -0.62                              
          speciesPotentilla pamerica        2.755e-03 5.249e-02   NaN -1.00 -1.00  0.62 -1.00                        
          speciesPrimula macrophylla        4.410e-04 2.100e-02   NaN -1.00 -1.00  0.62 -1.00  1.00                  
          speciesPsychrogeton andryaloides  8.150e-04 2.855e-02   NaN  1.00  1.00 -0.62  1.00 -1.00 -1.00            
          speciesSchistophyllidium bifurcum 3.639e-03 6.032e-02   NaN  1.00  1.00 -0.62  1.00 -1.00 -1.00  1.00      
          speciesWaldhemia tridactylites    6.230e-04 2.496e-02   NaN  1.00  1.00 -0.62  1.00 -1.00 -1.00  1.00  1.00
 Residual                                   4.576e-04 2.139e-02                                                      
Number of obs: 310, groups:  habitat, 5

Fixed effects:
                                  Estimate Std. Error         df t value Pr(>|t|)    
(Intercept)                      1.320e-01  3.627e-03  2.900e+02  36.398  < 2e-16 ***
habitatRuderal                  -1.361e-02  1.023e-02  3.068e+02  -1.330  0.18457    
habitatSemi-desert              -1.281e-02  1.023e-02  3.068e+02  -1.252  0.21166    
habitatSteppe                    6.537e-03  6.061e-03  2.920e+02   1.079  0.28165    
habitatSubnival                 -1.599e-02  7.683e-03  2.578e+02  -2.082  0.03836 *  
sampling_no2                    -1.571e-02  5.114e-03  3.070e+02  -3.073  0.00231 ** 
sampling_no3                    -2.060e-02  5.114e-03  3.070e+02  -4.028 7.09e-05 ***
sampling_no4                    -3.249e-02  5.114e-03  3.070e+02  -6.353 7.63e-10 ***
habitatRuderal:sampling_no2      2.431e-02  1.446e-02  3.070e+02   1.681  0.09378 .  
habitatSemi-desert:sampling_no2  2.791e-02  1.446e-02  3.070e+02   1.930  0.05454 .  
habitatSteppe:sampling_no2       3.954e-03  7.922e-03  3.070e+02   0.499  0.61804    
habitatSubnival:sampling_no2     2.763e-02  1.085e-02  3.070e+02   2.547  0.01136 *  
habitatRuderal:sampling_no3     -1.660e-02  1.446e-02  3.070e+02  -1.148  0.25200    
habitatSemi-desert:sampling_no3 -1.800e-02  1.446e-02  3.070e+02  -1.244  0.21428    
habitatSteppe:sampling_no3      -1.712e-02  7.922e-03  3.070e+02  -2.161  0.03147 *  
habitatSubnival:sampling_no3    -7.386e-03  1.085e-02  3.070e+02  -0.681  0.49649    
habitatRuderal:sampling_no4      3.049e-02  1.446e-02  3.070e+02   2.108  0.03587 *  
habitatSemi-desert:sampling_no4 -1.771e-02  1.446e-02  3.070e+02  -1.225  0.22162    
habitatSteppe:sampling_no4      -9.943e-04  7.922e-03  3.070e+02  -0.126  0.90021    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 19 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

fit warnings:
fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')````

````anova(M5)
Missing cells for: habitatSubnival:sampling_no1.  
Interpret type III hypotheses with care.
Type III Analysis of Variance Table with Satterthwaite's method
                      Sum Sq   Mean Sq NumDF  DenDF F value    Pr(>F)    
habitat             0.006643 0.0016608     4 217.20  3.6290 0.0069352 ** 
sampling_no         0.042669 0.0142230     3 306.97 31.0786 < 2.2e-16 ***
habitat:sampling_no 0.016647 0.0015134    11 306.97  3.3069 0.0002599 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

-1338.5 -1058.2 744.2 -1488.5 235

Scaled residuals: Min 1Q Median 3Q Max -3.0414 -0.5610 -0.0908 0.5200 3.2800

Random effects: Groups Name Variance Std.Dev. Corr
habitat (Intercept) 0.000e+00 0.000e+00
speciesArtemesia brevifolia 1.136e-03 3.371e-02 NaN
speciesAster flaccidus 9.169e-04 3.028e-02 NaN 1.00
speciesLactuca tatarica 2.085e-12 1.444e-06 NaN -0.62 -0.62
speciesLeontopodium ochroleucum 3.035e-03 5.509e-02 NaN 1.00 1.00 -0.62
speciesPotentilla pamerica 2.755e-03 5.249e-02 NaN -1.00 -1.00 0.62 -1.00
speciesPrimula macrophylla 4.410e-04 2.100e-02 NaN -1.00 -1.00 0.62 -1.00 1.00
speciesPsychrogeton andryaloides 8.150e-04 2.855e-02 NaN 1.00 1.00 -0.62 1.00 -1.00 -1.00
speciesSchistophyllidium bifurcum 3.639e-03 6.032e-02 NaN 1.00 1.00 -0.62 1.00 -1.00 -1.00 1.00
speciesWaldhemia tridactylites 6.230e-04 2.496e-02 NaN 1.00 1.00 -0.62 1.00 -1.00 -1.00 1.00 1.00 Residual 4.576e-04 2.139e-02
Number of obs: 310, groups: habitat, 5

Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 1.320e-01 3.627e-03 2.900e+02 36.398 < 2e-16 *** habitatRuderal -1.361e-02 1.023e-02 3.068e+02 -1.330 0.18457 habitatSemi-desert -1.281e-02 1.023e-02 3.068e+02 -1.252 0.21166 habitatSteppe 6.537e-03 6.061e-03 2.920e+02 1.079 0.28165 habitatSubnival -1.599e-02 7.683e-03 2.578e+02 -2.082 0.03836 * sampling_no2 -1.571e-02 5.114e-03 3.070e+02 -3.073 0.00231 ** sampling_no3 -2.060e-02 5.114e-03 3.070e+02 -4.028 7.09e-05 *** sampling_no4 -3.249e-02 5.114e-03 3.070e+02 -6.353 7.63e-10 *** habitatRuderal:sampling_no2 2.431e-02 1.446e-02 3.070e+02 1.681 0.09378 . habitatSemi-desert:sampling_no2 2.791e-02 1.446e-02 3.070e+02 1.930 0.05454 . habitatSteppe:sampling_no2 3.954e-03 7.922e-03 3.070e+02 0.499 0.61804 habitatSubnival:sampling_no2 2.763e-02 1.085e-02 3.070e+02 2.547 0.01136 * habitatRuderal:sampling_no3 -1.660e-02 1.446e-02 3.070e+02 -1.148 0.25200 habitatSemi-desert:sampling_no3 -1.800e-02 1.446e-02 3.070e+02 -1.244 0.21428 habitatSteppe:sampling_no3 -1.712e-02 7.922e-03 3.070e+02 -2.161 0.03147 * habitatSubnival:sampling_no3 -7.386e-03 1.085e-02 3.070e+02 -0.681 0.49649 habitatRuderal:sampling_no4 3.049e-02 1.446e-02 3.070e+02 2.108 0.03587 * habitatSemi-desert:sampling_no4 -1.771e-02 1.446e-02 3.070e+02 -1.225 0.22162 habitatSteppe:sampling_no4 -9.943e-04 7.922e-03 3.070e+02 -0.126 0.90021

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 19 > 12. Use print(x, correlation=TRUE) or vcov(x) if you need it

fit warnings: fixed-effect model matrix is rank deficient so dropping 1 column / coefficient optimizer (nloptwrap) convergence code: 0 (OK) boundary (singular) fit: see help('isSingular')""

""anova(M5) Missing cells for: habitatSubnival:sampling_no1. Interpret type III hypotheses with care. Type III Analysis of Variance Table with Satterthwaite's method Sum Sq Mean Sq NumDF DenDF F value Pr(>F) habitat 0.006643 0.0016608 4 217.20 3.6290 0.0069352 ** sampling_no 0.042669 0.0142230 3 306.97 31.0786 < 2.2e-16 *** habitat:sampling_no 0.016647 0.0015134 11 306.97 3.3069 0.0002599 ***

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1""

theThe habitat, sampling_no, and their interaction is significant. I have the following doubts:

i also tried other models such as ""M1 <- lmer(PhiPS2~habitat+(1|species), REML = F, data =physio2) ##(not significant) M2 <- lmer(PhiPS2~habitat+(1+habitat|species), REML=F, data =physio2) ##(not significant) M3 <- lmer(PhiPS2~habitat +sampling_no + (1|species), REML=F, data =physio2) (habitat = slightly significant, sampling_no = significant) M4 <- lmer(PhiPS2~habitatsampling_no + (1|species), REML=F, data =physio2) ##(habitat = slightly significant, sampling_no = significant, interaction = significant) M5 <- lmer(PhiPS2~habitatsampling_no +(1+ species|habitat), REML=F, data =physio2) ##(habitat = significant, sampling_no = significant, interaction = significant)""

M1 <- lmer(PhiPS2~habitat+(1|species), REML = F, data =physio2) ##(not significant)
M2 <- lmer(PhiPS2~habitat+(1+habitat|species), REML=F, data =physio2) ##(not significant)
M3 <- lmer(PhiPS2~habitat +sampling_no + (1|species), REML=F, data =physio2) (habitat = slightly significant, sampling_no = significant)
M4 <- lmer(PhiPS2~habitat*sampling_no + (1|species), REML=F, data =physio2) ##(habitat = slightly significant, sampling_no = significant, interaction = significant)
M5 <- lmer(PhiPS2~habitat*sampling_no +(1+ species|habitat), REML=F, data =physio2) ##(habitat = significant, sampling_no = significant, interaction = significant)

I tried using a linear mixed-effect model: ""M5 <- lmer(PhiPS2~habitat*sampling_no + (1+ species|habitat), REML=F, data =physio2)"" ""summary(M5) Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: PhiPS2 ~ habitat * sampling_no + (1 + species | habitat) Data: physio2

 AIC      BIC   logLik deviance df.resid

-1338.5 -1058.2 744.2 -1488.5 235

Scaled residuals: Min 1Q Median 3Q Max -3.0414 -0.5610 -0.0908 0.5200 3.2800

Random effects: Groups Name Variance Std.Dev. Corr
habitat (Intercept) 0.000e+00 0.000e+00
speciesArtemesia brevifolia 1.136e-03 3.371e-02 NaN
speciesAster flaccidus 9.169e-04 3.028e-02 NaN 1.00
speciesLactuca tatarica 2.085e-12 1.444e-06 NaN -0.62 -0.62
speciesLeontopodium ochroleucum 3.035e-03 5.509e-02 NaN 1.00 1.00 -0.62
speciesPotentilla pamerica 2.755e-03 5.249e-02 NaN -1.00 -1.00 0.62 -1.00
speciesPrimula macrophylla 4.410e-04 2.100e-02 NaN -1.00 -1.00 0.62 -1.00 1.00
speciesPsychrogeton andryaloides 8.150e-04 2.855e-02 NaN 1.00 1.00 -0.62 1.00 -1.00 -1.00
speciesSchistophyllidium bifurcum 3.639e-03 6.032e-02 NaN 1.00 1.00 -0.62 1.00 -1.00 -1.00 1.00
speciesWaldhemia tridactylites 6.230e-04 2.496e-02 NaN 1.00 1.00 -0.62 1.00 -1.00 -1.00 1.00 1.00 Residual 4.576e-04 2.139e-02
Number of obs: 310, groups: habitat, 5

Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 1.320e-01 3.627e-03 2.900e+02 36.398 < 2e-16 *** habitatRuderal -1.361e-02 1.023e-02 3.068e+02 -1.330 0.18457 habitatSemi-desert -1.281e-02 1.023e-02 3.068e+02 -1.252 0.21166 habitatSteppe 6.537e-03 6.061e-03 2.920e+02 1.079 0.28165 habitatSubnival -1.599e-02 7.683e-03 2.578e+02 -2.082 0.03836 * sampling_no2 -1.571e-02 5.114e-03 3.070e+02 -3.073 0.00231 ** sampling_no3 -2.060e-02 5.114e-03 3.070e+02 -4.028 7.09e-05 *** sampling_no4 -3.249e-02 5.114e-03 3.070e+02 -6.353 7.63e-10 *** habitatRuderal:sampling_no2 2.431e-02 1.446e-02 3.070e+02 1.681 0.09378 . habitatSemi-desert:sampling_no2 2.791e-02 1.446e-02 3.070e+02 1.930 0.05454 . habitatSteppe:sampling_no2 3.954e-03 7.922e-03 3.070e+02 0.499 0.61804 habitatSubnival:sampling_no2 2.763e-02 1.085e-02 3.070e+02 2.547 0.01136 * habitatRuderal:sampling_no3 -1.660e-02 1.446e-02 3.070e+02 -1.148 0.25200 habitatSemi-desert:sampling_no3 -1.800e-02 1.446e-02 3.070e+02 -1.244 0.21428 habitatSteppe:sampling_no3 -1.712e-02 7.922e-03 3.070e+02 -2.161 0.03147 * habitatSubnival:sampling_no3 -7.386e-03 1.085e-02 3.070e+02 -0.681 0.49649 habitatRuderal:sampling_no4 3.049e-02 1.446e-02 3.070e+02 2.108 0.03587 * habitatSemi-desert:sampling_no4 -1.771e-02 1.446e-02 3.070e+02 -1.225 0.22162 habitatSteppe:sampling_no4 -9.943e-04 7.922e-03 3.070e+02 -0.126 0.90021

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 19 > 12. Use print(x, correlation=TRUE) or vcov(x) if you need it

fit warnings: fixed-effect model matrix is rank deficient so dropping 1 column / coefficient optimizer (nloptwrap) convergence code: 0 (OK) boundary (singular) fit: see help('isSingular')""

""anova(M5) Missing cells for: habitatSubnival:sampling_no1. Interpret type III hypotheses with care. Type III Analysis of Variance Table with Satterthwaite's method Sum Sq Mean Sq NumDF DenDF F value Pr(>F) habitat 0.006643 0.0016608 4 217.20 3.6290 0.0069352 ** sampling_no 0.042669 0.0142230 3 306.97 31.0786 < 2.2e-16 *** habitat:sampling_no 0.016647 0.0015134 11 306.97 3.3069 0.0002599 ***

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1""

the habitat, sampling_no, and their interaction is significant. I have the following doubts:

i also tried other models such as ""M1 <- lmer(PhiPS2~habitat+(1|species), REML = F, data =physio2) ##(not significant) M2 <- lmer(PhiPS2~habitat+(1+habitat|species), REML=F, data =physio2) ##(not significant) M3 <- lmer(PhiPS2~habitat +sampling_no + (1|species), REML=F, data =physio2) (habitat = slightly significant, sampling_no = significant) M4 <- lmer(PhiPS2~habitatsampling_no + (1|species), REML=F, data =physio2) ##(habitat = slightly significant, sampling_no = significant, interaction = significant) M5 <- lmer(PhiPS2~habitatsampling_no +(1+ species|habitat), REML=F, data =physio2) ##(habitat = significant, sampling_no = significant, interaction = significant)""

I tried using a linear mixed-effect model: M5 <- lmer(PhiPS2~habitat*sampling_no + (1+ species|habitat), REML=F, data =physio2)

Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: PhiPS2 ~ habitat * sampling_no + (1 + species | habitat)
   Data: physio2

     AIC      BIC   logLik deviance df.resid 
 -1338.5  -1058.2    744.2  -1488.5      235 

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-3.0414 -0.5610 -0.0908  0.5200  3.2800 

Random effects:
 Groups   Name                              Variance  Std.Dev.  Corr                                                 
 habitat  (Intercept)                       0.000e+00 0.000e+00                                                      
          speciesArtemesia brevifolia       1.136e-03 3.371e-02   NaN                                                
          speciesAster flaccidus            9.169e-04 3.028e-02   NaN  1.00                                          
          speciesLactuca tatarica           2.085e-12 1.444e-06   NaN -0.62 -0.62                                    
          speciesLeontopodium ochroleucum   3.035e-03 5.509e-02   NaN  1.00  1.00 -0.62                              
          speciesPotentilla pamerica        2.755e-03 5.249e-02   NaN -1.00 -1.00  0.62 -1.00                        
          speciesPrimula macrophylla        4.410e-04 2.100e-02   NaN -1.00 -1.00  0.62 -1.00  1.00                  
          speciesPsychrogeton andryaloides  8.150e-04 2.855e-02   NaN  1.00  1.00 -0.62  1.00 -1.00 -1.00            
          speciesSchistophyllidium bifurcum 3.639e-03 6.032e-02   NaN  1.00  1.00 -0.62  1.00 -1.00 -1.00  1.00      
          speciesWaldhemia tridactylites    6.230e-04 2.496e-02   NaN  1.00  1.00 -0.62  1.00 -1.00 -1.00  1.00  1.00
 Residual                                   4.576e-04 2.139e-02                                                      
Number of obs: 310, groups:  habitat, 5

Fixed effects:
                                  Estimate Std. Error         df t value Pr(>|t|)    
(Intercept)                      1.320e-01  3.627e-03  2.900e+02  36.398  < 2e-16 ***
habitatRuderal                  -1.361e-02  1.023e-02  3.068e+02  -1.330  0.18457    
habitatSemi-desert              -1.281e-02  1.023e-02  3.068e+02  -1.252  0.21166    
habitatSteppe                    6.537e-03  6.061e-03  2.920e+02   1.079  0.28165    
habitatSubnival                 -1.599e-02  7.683e-03  2.578e+02  -2.082  0.03836 *  
sampling_no2                    -1.571e-02  5.114e-03  3.070e+02  -3.073  0.00231 ** 
sampling_no3                    -2.060e-02  5.114e-03  3.070e+02  -4.028 7.09e-05 ***
sampling_no4                    -3.249e-02  5.114e-03  3.070e+02  -6.353 7.63e-10 ***
habitatRuderal:sampling_no2      2.431e-02  1.446e-02  3.070e+02   1.681  0.09378 .  
habitatSemi-desert:sampling_no2  2.791e-02  1.446e-02  3.070e+02   1.930  0.05454 .  
habitatSteppe:sampling_no2       3.954e-03  7.922e-03  3.070e+02   0.499  0.61804    
habitatSubnival:sampling_no2     2.763e-02  1.085e-02  3.070e+02   2.547  0.01136 *  
habitatRuderal:sampling_no3     -1.660e-02  1.446e-02  3.070e+02  -1.148  0.25200    
habitatSemi-desert:sampling_no3 -1.800e-02  1.446e-02  3.070e+02  -1.244  0.21428    
habitatSteppe:sampling_no3      -1.712e-02  7.922e-03  3.070e+02  -2.161  0.03147 *  
habitatSubnival:sampling_no3    -7.386e-03  1.085e-02  3.070e+02  -0.681  0.49649    
habitatRuderal:sampling_no4      3.049e-02  1.446e-02  3.070e+02   2.108  0.03587 *  
habitatSemi-desert:sampling_no4 -1.771e-02  1.446e-02  3.070e+02  -1.225  0.22162    
habitatSteppe:sampling_no4      -9.943e-04  7.922e-03  3.070e+02  -0.126  0.90021    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 19 > 12.
Use print(x, correlation=TRUE)  or
    vcov(x)        if you need it

fit warnings:
fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')````

````anova(M5)
Missing cells for: habitatSubnival:sampling_no1.  
Interpret type III hypotheses with care.
Type III Analysis of Variance Table with Satterthwaite's method
                      Sum Sq   Mean Sq NumDF  DenDF F value    Pr(>F)    
habitat             0.006643 0.0016608     4 217.20  3.6290 0.0069352 ** 
sampling_no         0.042669 0.0142230     3 306.97 31.0786 < 2.2e-16 ***
habitat:sampling_no 0.016647 0.0015134    11 306.97  3.3069 0.0002599 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The habitat, sampling_no, and their interaction is significant. I have the following doubts:

i also tried other models such as

M1 <- lmer(PhiPS2~habitat+(1|species), REML = F, data =physio2) ##(not significant)
M2 <- lmer(PhiPS2~habitat+(1+habitat|species), REML=F, data =physio2) ##(not significant)
M3 <- lmer(PhiPS2~habitat +sampling_no + (1|species), REML=F, data =physio2) (habitat = slightly significant, sampling_no = significant)
M4 <- lmer(PhiPS2~habitat*sampling_no + (1|species), REML=F, data =physio2) ##(habitat = slightly significant, sampling_no = significant, interaction = significant)
M5 <- lmer(PhiPS2~habitat*sampling_no +(1+ species|habitat), REML=F, data =physio2) ##(habitat = significant, sampling_no = significant, interaction = significant)
added 4 characters in body
Source Link
scholar101
scholar101
  • 73
  • 3

I tried using a linear mixed-effect model: ""M5 <- lmer(PhiPS2~habitat*sampling_no + (1+ species|habitat), REML=F, data =physio2)"" ""summary(M5) Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: PhiPS2 ~ habitat * sampling_no + (1 + species | habitat) Data: physio2

summary(M5) Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: PhiPS2 ~ habitat * sampling_no + (1 + species | habitat) Data: physio2

fit warnings: fixed-effect model matrix is rank deficient so dropping 1 column / coefficient optimizer (nloptwrap) convergence code: 0 (OK) boundary (singular) fit: see help('isSingular')""

anova""anova(M5) Missing cells for: habitatSubnival:sampling_no1. Interpret type III hypotheses with care. Type III Analysis of Variance Table with Satterthwaite's method Sum Sq Mean Sq NumDF DenDF F value Pr(>F) habitat 0.006643 0.0016608 4 217.20 3.6290 0.0069352 ** sampling_no 0.042669 0.0142230 3 306.97 31.0786 < 2.2e-16 *** habitat:sampling_no 0.016647 0.0015134 11 306.97 3.3069 0.0002599 ***

I tried using a linear mixed-effect model: ""M5 <- lmer(PhiPS2~habitat*sampling_no + (1+ species|habitat), REML=F, data =physio2)

summary(M5) Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: PhiPS2 ~ habitat * sampling_no + (1 + species | habitat) Data: physio2

fit warnings: fixed-effect model matrix is rank deficient so dropping 1 column / coefficient optimizer (nloptwrap) convergence code: 0 (OK) boundary (singular) fit: see help('isSingular')

anova(M5) Missing cells for: habitatSubnival:sampling_no1. Interpret type III hypotheses with care. Type III Analysis of Variance Table with Satterthwaite's method Sum Sq Mean Sq NumDF DenDF F value Pr(>F) habitat 0.006643 0.0016608 4 217.20 3.6290 0.0069352 ** sampling_no 0.042669 0.0142230 3 306.97 31.0786 < 2.2e-16 *** habitat:sampling_no 0.016647 0.0015134 11 306.97 3.3069 0.0002599 ***

I tried using a linear mixed-effect model: ""M5 <- lmer(PhiPS2~habitat*sampling_no + (1+ species|habitat), REML=F, data =physio2)"" ""summary(M5) Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: PhiPS2 ~ habitat * sampling_no + (1 + species | habitat) Data: physio2

fit warnings: fixed-effect model matrix is rank deficient so dropping 1 column / coefficient optimizer (nloptwrap) convergence code: 0 (OK) boundary (singular) fit: see help('isSingular')""

""anova(M5) Missing cells for: habitatSubnival:sampling_no1. Interpret type III hypotheses with care. Type III Analysis of Variance Table with Satterthwaite's method Sum Sq Mean Sq NumDF DenDF F value Pr(>F) habitat 0.006643 0.0016608 4 217.20 3.6290 0.0069352 ** sampling_no 0.042669 0.0142230 3 306.97 31.0786 < 2.2e-16 *** habitat:sampling_no 0.016647 0.0015134 11 306.97 3.3069 0.0002599 ***

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scholar101
scholar101
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How to interpret and visualise output from lmer model r?

I have data from 310 individual plants, from various habitats (5 type), species (10) occuring in different habitats, measured photosynthesis performance (PhiPS2) in different months (sampling_no_).

I aim to look at

  1. how the PhiPS2 value varies with habitat and months(sampling_no). And since I have different species, I think I should consider looking at
  2. how it changes with different species in different habitats and months (sampling_no). I have PhiPS2 as a numeric continuous variable and habitat and sampling_no as categorical values.

I tried using a linear mixed-effect model: ""M5 <- lmer(PhiPS2~habitat*sampling_no + (1+ species|habitat), REML=F, data =physio2)

summary(M5) Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest'] Formula: PhiPS2 ~ habitat * sampling_no + (1 + species | habitat) Data: physio2

 AIC      BIC   logLik deviance df.resid

-1338.5 -1058.2 744.2 -1488.5 235

Scaled residuals: Min 1Q Median 3Q Max -3.0414 -0.5610 -0.0908 0.5200 3.2800

Random effects: Groups Name Variance Std.Dev. Corr
habitat (Intercept) 0.000e+00 0.000e+00
speciesArtemesia brevifolia 1.136e-03 3.371e-02 NaN
speciesAster flaccidus 9.169e-04 3.028e-02 NaN 1.00
speciesLactuca tatarica 2.085e-12 1.444e-06 NaN -0.62 -0.62
speciesLeontopodium ochroleucum 3.035e-03 5.509e-02 NaN 1.00 1.00 -0.62
speciesPotentilla pamerica 2.755e-03 5.249e-02 NaN -1.00 -1.00 0.62 -1.00
speciesPrimula macrophylla 4.410e-04 2.100e-02 NaN -1.00 -1.00 0.62 -1.00 1.00
speciesPsychrogeton andryaloides 8.150e-04 2.855e-02 NaN 1.00 1.00 -0.62 1.00 -1.00 -1.00
speciesSchistophyllidium bifurcum 3.639e-03 6.032e-02 NaN 1.00 1.00 -0.62 1.00 -1.00 -1.00 1.00
speciesWaldhemia tridactylites 6.230e-04 2.496e-02 NaN 1.00 1.00 -0.62 1.00 -1.00 -1.00 1.00 1.00 Residual 4.576e-04 2.139e-02
Number of obs: 310, groups: habitat, 5

Fixed effects: Estimate Std. Error df t value Pr(>|t|) (Intercept) 1.320e-01 3.627e-03 2.900e+02 36.398 < 2e-16 *** habitatRuderal -1.361e-02 1.023e-02 3.068e+02 -1.330 0.18457 habitatSemi-desert -1.281e-02 1.023e-02 3.068e+02 -1.252 0.21166 habitatSteppe 6.537e-03 6.061e-03 2.920e+02 1.079 0.28165 habitatSubnival -1.599e-02 7.683e-03 2.578e+02 -2.082 0.03836 * sampling_no2 -1.571e-02 5.114e-03 3.070e+02 -3.073 0.00231 ** sampling_no3 -2.060e-02 5.114e-03 3.070e+02 -4.028 7.09e-05 *** sampling_no4 -3.249e-02 5.114e-03 3.070e+02 -6.353 7.63e-10 *** habitatRuderal:sampling_no2 2.431e-02 1.446e-02 3.070e+02 1.681 0.09378 . habitatSemi-desert:sampling_no2 2.791e-02 1.446e-02 3.070e+02 1.930 0.05454 . habitatSteppe:sampling_no2 3.954e-03 7.922e-03 3.070e+02 0.499 0.61804 habitatSubnival:sampling_no2 2.763e-02 1.085e-02 3.070e+02 2.547 0.01136 * habitatRuderal:sampling_no3 -1.660e-02 1.446e-02 3.070e+02 -1.148 0.25200 habitatSemi-desert:sampling_no3 -1.800e-02 1.446e-02 3.070e+02 -1.244 0.21428 habitatSteppe:sampling_no3 -1.712e-02 7.922e-03 3.070e+02 -2.161 0.03147 * habitatSubnival:sampling_no3 -7.386e-03 1.085e-02 3.070e+02 -0.681 0.49649 habitatRuderal:sampling_no4 3.049e-02 1.446e-02 3.070e+02 2.108 0.03587 * habitatSemi-desert:sampling_no4 -1.771e-02 1.446e-02 3.070e+02 -1.225 0.22162 habitatSteppe:sampling_no4 -9.943e-04 7.922e-03 3.070e+02 -0.126 0.90021

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation matrix not shown by default, as p = 19 > 12. Use print(x, correlation=TRUE) or vcov(x) if you need it

fit warnings: fixed-effect model matrix is rank deficient so dropping 1 column / coefficient optimizer (nloptwrap) convergence code: 0 (OK) boundary (singular) fit: see help('isSingular')

anova(M5) Missing cells for: habitatSubnival:sampling_no1. Interpret type III hypotheses with care. Type III Analysis of Variance Table with Satterthwaite's method Sum Sq Mean Sq NumDF DenDF F value Pr(>F) habitat 0.006643 0.0016608 4 217.20 3.6290 0.0069352 ** sampling_no 0.042669 0.0142230 3 306.97 31.0786 < 2.2e-16 *** habitat:sampling_no 0.016647 0.0015134 11 306.97 3.3069 0.0002599 ***

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1""

the habitat, sampling_no, and their interaction is significant. I have the following doubts:

Is the model I used correct for my purpose? if yes, how to interpret the result, and graphically represnt it? How do I model/graphically represnt the species level differences? I have not done any transformation of the response variable, is it needed? i am not sure.

i also tried other models such as ""M1 <- lmer(PhiPS2~habitat+(1|species), REML = F, data =physio2) ##(not significant) M2 <- lmer(PhiPS2~habitat+(1+habitat|species), REML=F, data =physio2) ##(not significant) M3 <- lmer(PhiPS2~habitat +sampling_no + (1|species), REML=F, data =physio2) (habitat = slightly significant, sampling_no = significant) M4 <- lmer(PhiPS2~habitatsampling_no + (1|species), REML=F, data =physio2) ##(habitat = slightly significant, sampling_no = significant, interaction = significant) M5 <- lmer(PhiPS2~habitatsampling_no +(1+ species|habitat), REML=F, data =physio2) ##(habitat = significant, sampling_no = significant, interaction = significant)""

Please suggest. Thanks