Morphological and mechanical properties of indigenous bamboo species

Data Import

df<-Complete_Summarized_Data_Bamboo
df

Inspect for NAs - Aligned Rank Transform won’t run otherwise!

which(is.na(df), arr.ind=TRUE)

     row col

Convert variables into factors

df$Location <- factor(df$Location)
df$Species <- factor(df$Species)

Check ANOVA assumptions

Run Shapiro-Wilk’s Test to test for normality.

df%>%shapiro_test(CWT, CD, MOE, MOR, MVS, GSG, FSPL, MaxStress)

Only CWT (Culm Wall Thickness) seems to satisfy the normality assumption. We can proceed with ANOVA for CWT; rest of the variables will be passed to ART (Aligned Rank Transformation) ANOVA, a non-parametric approach to factorial ANOVA.

Run a two-way ANOVA for Culm Wall Thickness

We now proceed to analyzing CWT using regular ANOVA. We detect a strong interaction effect for Species x Location.

lm.cwt <-lm(CWT ~ Species * Location + (1|Sample), data=df) 
anova(lm.cwt)

Analysis of Variance Table

Response: CWT
                 Df  Sum Sq Mean Sq F value    Pr(>F)    
Species           2 191.222  95.611 96.8085 < 2.2e-16 ***
Location          4  11.617   2.904  2.9406   0.02686 *  
Species:Location  6  49.245   8.208  8.3103 1.083e-06 ***
Residuals        65  64.196   0.988                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Run an ART ANOVA for CD, MOE, MOR, SpGrav, FSPL, MVS, and MaxStress

Now, we run ART-ANOVA for the rest of the variables in the data frame.

 lm.cd <- art(CD ~ Species * Location + (1|Sample), data=df)
anova(lm.cd)

Analysis of Variance of Aligned Rank Transformed Data

Table Type: Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df) 
Model: Mixed Effects (lmer)
Response: art(CD)

                         F Df Df.res     Pr(>F)    
1 Species           8.5699  2     63  0.0005105 ***
2 Location         10.7778  4     63 1.0176e-06 ***
3 Species:Location  9.5626  6     63 1.8359e-07 ***
---
Signif. codes:   0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

plot(cd.plot.fig)

Generate pairwise comparisons across Species within Location: Culm Diameter

  # 'Species' is a column in the data frame
unique_species <- unique(df$Species)

# Initialize an empty list to store the results for each species
cld_results_list <- list()

# Loop through each species
for (species in unique_species) {
  # Subset data for the current species
  subset_species <- filter(df, Species == species)
  
  # Fit an art model for the current species
  art_model <- art(formula = CD ~ Location, data = subset_species)
  
  # Perform contrasts for the main effects of Location using art.con()
  marginal <- art.con(art_model, "Location")
  
  # Convert to data frame
  marginal_df <- as.data.frame(marginal)
  
  # Perform post-hoc comparisons and store the results in the list
  cld_results_list[[species]] <- cldList(p.value ~ contrast, data = marginal_df)
}

# Access the results for a specific species
cld_results_list$"Tinik"

cld_results_list$"Giant"

cld_results_list$"Bolo"

lm.moe <- art(MOE ~ Species * Location + (1|Sample), data=df) 
anova(lm.moe)

Analysis of Variance of Aligned Rank Transformed Data

Table Type: Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df) 
Model: Mixed Effects (lmer)
Response: art(MOE)

                         F Df Df.res     Pr(>F)    
1 Species           6.0788  2     63  0.0038556  **
2 Location         14.1179  4     63 2.7956e-08 ***
3 Species:Location 15.2145  6     63 1.1100e-10 ***
---
Signif. codes:   0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

plot(moe.plot.fig)

# 'Species' is a column in the data frame
unique_species <- unique(df$Species)

# Initialize an empty list to store the results for each species
cld_results_list <- list()

# Loop through each species
for (species in unique_species) {
  # Subset data for the current species
  subset_species <- filter(df, Species == species)
  
  # Fit an art model for the current species
  art_model <- art(formula = MOE ~ Location, data = subset_species)
  
  # Perform contrasts for the main effects of Location using art.con()
  marginal <- art.con(art_model, "Location")
  
  # Convert to data frame
  marginal_df <- as.data.frame(marginal)
  
  # Perform post-hoc comparisons and store the results in the list
  cld_results_list[[species]] <- cldList(p.value ~ contrast, data = marginal_df)
}

# Access the results for a specific species
cld_results_list$"Tinik"

cld_results_list$"Giant"

cld_results_list$"Bolo"

lm.mor <- art(MOR ~ Species * Location + (1|Sample), data=df)
anova(lm.mor)

Analysis of Variance of Aligned Rank Transformed Data

Table Type: Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df) 
Model: Mixed Effects (lmer)
Response: art(MOR)

                         F Df Df.res     Pr(>F)    
1 Species           2.6638  2     63   0.077528   .
2 Location          9.3363  4     63 5.4538e-06 ***
3 Species:Location 10.8956  6     63 2.7399e-08 ***
---
Signif. codes:   0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

plot(mor.plot.fig)

# 'Species' is a column in the data frame
unique_species <- unique(df$Species)

# Initialize an empty list to store the results for each species
cld_results_list <- list()

# Loop through each species
for (species in unique_species) {
  # Subset data for the current species
  subset_species <- filter(df, Species == species)
  
  # Fit an art model for the current species
  art_model <- art(formula = MOR ~ Location, data = subset_species)
  
  # Perform contrasts for the main effects of Location using art.con()
  marginal <- art.con(art_model, "Location")
  
  # Convert to data frame
  marginal_df <- as.data.frame(marginal)
  
  # Perform post-hoc comparisons and store the results in the list
  cld_results_list[[species]] <- cldList(p.value ~ contrast, data = marginal_df)
}

# Access the results for a specific species
cld_results_list$"Tinik"

cld_results_list$"Giant"

cld_results_list$"Bolo"

lm.gsg <- art(GSG ~ Species * Location + (1|Sample), data=df)
anova(lm.gsg)

Analysis of Variance of Aligned Rank Transformed Data

Table Type: Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df) 
Model: Mixed Effects (lmer)
Response: art(GSG)

                         F Df Df.res    Pr(>F)   
1 Species          0.26865  2     63 0.7652786   
2 Location         4.71671  4     63 0.0021541 **
3 Species:Location 2.73439  6     63 0.0200236  *
---
Signif. codes:   0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

plot(gsg.plot.fig)

# 'Species' is a column in the data frame
unique_species <- unique(df$Species)

# Initialize an empty list to store the results for each species
cld_results_list <- list()

# Loop through each species
for (species in unique_species) {
  # Subset data for the current species
  subset_species <- filter(df, Species == species)
  
  # Fit an art model for the current species
  art_model <- art(formula = GSG ~ Location, data = subset_species)
  
  # Perform contrasts for the main effects of Location using art.con()
  marginal <- art.con(art_model, "Location")
  
  # Convert to data frame
  marginal_df <- as.data.frame(marginal)
  
  # Perform post-hoc comparisons and store the results in the list
  cld_results_list[[species]] <- cldList(p.value ~ contrast, data = marginal_df)
}

# Access the results for a specific species
cld_results_list$"Tinik"

cld_results_list$"Giant"

cld_results_list$"Bolo"

lm.fspl <- art(FSPL ~ Species * Location + (1|Sample), data=df)
anova(lm.fspl)

Analysis of Variance of Aligned Rank Transformed Data

Table Type: Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df) 
Model: Mixed Effects (lmer)
Response: art(FSPL)

                        F Df Df.res     Pr(>F)    
1 Species          1.1738  2     63  0.3158545    
2 Location         4.8432  4     63  0.0018062  **
3 Species:Location 7.8765  6     63 2.3921e-06 ***
---
Signif. codes:   0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

plot(fspl.plot.fig)

# 'Species' is a column in the data frame
unique_species <- unique(df$Species)

# Initialize an empty list to store the results for each species
cld_results_list <- list()

# Loop through each species
for (species in unique_species) {
  # Subset data for the current species
  subset_species <- filter(df, Species == species)
  
  # Fit an art model for the current species
  art_model <- art(formula = FSPL ~ Location, data = subset_species)
  
  # Perform contrasts for the main effects of Location using art.con()
  marginal <- art.con(art_model, "Location")
  
  # Convert to data frame
  marginal_df <- as.data.frame(marginal)
  
  # Perform post-hoc comparisons and store the results in the list
  cld_results_list[[species]] <- cldList(p.value ~ contrast, data = marginal_df)
}

# Access the results for a specific species
cld_results_list$"Tinik"

cld_results_list$"Giant"

cld_results_list$"Bolo"

lm.stress <- art(MaxStress ~ Species * Location + (1|Sample), data=df)
anova(lm.stress)

Analysis of Variance of Aligned Rank Transformed Data

Table Type: Analysis of Deviance Table (Type III Wald F tests with Kenward-Roger df) 
Model: Mixed Effects (lmer)
Response: art(MaxStress)

                        F Df Df.res     Pr(>F)    
1 Species          1.0516  2     63 0.35541314    
2 Location         8.1105  4     63 2.4316e-05 ***
3 Species:Location 5.5986  6     63 0.00010521 ***
---
Signif. codes:   0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

plot(stress.plot.fig)

# 'Species' is a column in the data frame
unique_species <- unique(df$Species)

# Initialize an empty list to store the results for each species
cld_results_list <- list()

# Loop through each species
for (species in unique_species) {
  # Subset data for the current species
  subset_species <- filter(df, Species == species)
  
  # Fit an art model for the current species
  art_model <- art(formula = MaxStress ~ Location, data = subset_species)
  
  # Perform contrasts for the main effects of Location using art.con()
  marginal <- art.con(art_model, "Location")
  
  # Convert to data frame
  marginal_df <- as.data.frame(marginal)
  
  # Perform post-hoc comparisons and store the results in the list
  cld_results_list[[species]] <- cldList(p.value ~ contrast, data = marginal_df)
}

# Access the results for a specific species
cld_results_list$"Tinik"

cld_results_list$"Giant"

cld_results_list$"Bolo"