PCA for matury model

I am going to use R for PCA in the data Sandra. I am reading the data from csv file.

lean<-read.csv("matrix1.csv",stringsAsFactors = F, header=T)
lean1<-lean[1:101,1:48]
#str(lean) #allows you to see an overview class,levels of dataframe
#sapply(lean1,class) # class of variables

names of variables

names(lean1)

 [1] "Lean.culture"                                                                   
 [2] "Values.and.personal.vision"                                                     
 [3] "Way.of.thinking"                                                                
 [4] "People.skills"                                                                  
 [5] "Growth.in.the.philosophy"                                                       
 [6] "Growth.and.development.of.Lean.leaders"                                         
 [7] "Promotion.and.continuous.development.of.Lean.Construction"                      
 [8] "Encourage.of.continuous.improvement"                                            
 [9] "Growth.and.development.of.the.team.work"                                        
[10] "Team.work.processes"                                                            
[11] "Problem.understanding"                                                          
[12] "Solution.and.joint.learning"                                                    
[13] "Fulfillment.of.the.value.offer"                                                 
[14] "Continuous.improvement"                                                         
[15] "Control.of.complete.process"                                                    
[16] "Development.and.operation.of..planning.and.control.system.of.production"        
[17] "Pull.system.development"                                                        
[18] "Implementation.of.a.quality.management.and.control.system"                      
[19] "Knowledge.and.selection.of.lean.construction.tools"                             
[20] "Level.of.using.Lean.Construction.tools"                                         
[21] "Simplification.of.processes"                                                    
[22] "Flexibility"                                                                    
[23] "Transparency"                                                                   
[24] "Benchmarking"                                                                   
[25] "Continuous.flow"                                                                
[26] "Waste.reduction"                                                                
[27] "Variability.reduction"                                                          
[28] "Cycle.time.reduction"                                                           
[29] "Standards.development"                                                          
[30] "Improvement.and.sustainability.of.standards"                                    
[31] "Engage.with.the.safety.at.the.workplace"                                        
[32] "Learning.and.training.for.safety.at.the.workplace"                              
[33] "Integration.of.new.developments"                                                
[34] "Knowledge.management"                                                           
[35] "Continuous.support.for.the.development.of.a.lean.construction.production.system"
[36] "Definition.and.deployment.of.policy.and.strategy.for..lean.construction.support"
[37] "Focus.on.philosophy"                                                            
[38] "Involvement.of.People"                                                          
[39] "Interaction.in.the.work.environment"                                            
[40] "Work.environment.construction"                                                  
[41] "Business.outcomes"                                                              
[42] "Project.support.by.using.the..enterprise.processes"                             
[43] "Implementation.of.Management.system"                                            
[44] "Contractual.management.process"                                                 
[45] "systems.of.Information"                                                         
[46] "Flow.of.information"                                                            
[47] "Supply.chain.management"                                                        
[48] "Logistic.operations"                                                            

summary(lean_PCA)

Importance of components%s:
                          PC1     PC2
Standard deviation     4.3273 2.11606
Proportion of Variance 0.3901 0.09329
Cumulative Proportion  0.3901 0.48339
                           PC3     PC4
Standard deviation     1.66039 1.48825
Proportion of Variance 0.05744 0.04614
Cumulative Proportion  0.54083 0.58697
                           PC5     PC6
Standard deviation     1.38007 1.27298
Proportion of Variance 0.03968 0.03376
Cumulative Proportion  0.62665 0.66041
                           PC7     PC8
Standard deviation     1.17191 1.11677
Proportion of Variance 0.02861 0.02598
Cumulative Proportion  0.68902 0.71501
                           PC9    PC10
Standard deviation     1.07156 1.02454
Proportion of Variance 0.02392 0.02187
Cumulative Proportion  0.73893 0.76080
                          PC11    PC12
Standard deviation     0.97299 0.91275
Proportion of Variance 0.01972 0.01736
Cumulative Proportion  0.78052 0.79788
                          PC13    PC14
Standard deviation     0.86621 0.82283
Proportion of Variance 0.01563 0.01411
Cumulative Proportion  0.81351 0.82761
                          PC15    PC16
Standard deviation     0.81315 0.78461
Proportion of Variance 0.01378 0.01283
Cumulative Proportion  0.84139 0.85421
                          PC17    PC18
Standard deviation     0.75423 0.71818
Proportion of Variance 0.01185 0.01075
Cumulative Proportion  0.86607 0.87681
                          PC19    PC20
Standard deviation     0.70931 0.66475
Proportion of Variance 0.01048 0.00921
Cumulative Proportion  0.88729 0.89650
                          PC21    PC22
Standard deviation     0.64380 0.61902
Proportion of Variance 0.00864 0.00798
Cumulative Proportion  0.90513 0.91312
                          PC23    PC24
Standard deviation     0.60426 0.58007
Proportion of Variance 0.00761 0.00701
Cumulative Proportion  0.92072 0.92773
                          PC25    PC26
Standard deviation     0.56017 0.53505
Proportion of Variance 0.00654 0.00596
Cumulative Proportion  0.93427 0.94023
                         PC27    PC28
Standard deviation     0.5185 0.51101
Proportion of Variance 0.0056 0.00544
Cumulative Proportion  0.9458 0.95127
                          PC29    PC30
Standard deviation     0.48689 0.46641
Proportion of Variance 0.00494 0.00453
Cumulative Proportion  0.95621 0.96075
                          PC31    PC32
Standard deviation     0.43408 0.42391
Proportion of Variance 0.00393 0.00374
Cumulative Proportion  0.96467 0.96842
                          PC33    PC34
Standard deviation     0.42060 0.40230
Proportion of Variance 0.00369 0.00337
Cumulative Proportion  0.97210 0.97547
                          PC35    PC36
Standard deviation     0.38346 0.37427
Proportion of Variance 0.00306 0.00292
Cumulative Proportion  0.97854 0.98145
                          PC37    PC38
Standard deviation     0.34577 0.32569
Proportion of Variance 0.00249 0.00221
Cumulative Proportion  0.98394 0.98615
                         PC39    PC40
Standard deviation     0.3176 0.31370
Proportion of Variance 0.0021 0.00205
Cumulative Proportion  0.9883 0.99031
                          PC41    PC42
Standard deviation     0.29461 0.28039
Proportion of Variance 0.00181 0.00164
Cumulative Proportion  0.99211 0.99375
                          PC43    PC44
Standard deviation     0.25410 0.24814
Proportion of Variance 0.00135 0.00128
Cumulative Proportion  0.99510 0.99638
                          PC45   PC46
Standard deviation     0.23282 0.2196
Proportion of Variance 0.00113 0.0010
Cumulative Proportion  0.99751 0.9985
                          PC47    PC48
Standard deviation     0.20887 0.16641
Proportion of Variance 0.00091 0.00058
Cumulative Proportion  0.99942 1.00000

the first 20 principal components explain 90.5% of the variation. You can also limit the number of component to that number that accounts for a certain fraction of the total variance. For example, if you are satisfied with 70% of the total variance explained then use the number of components to achieve that.

This is the loadings of the PCA. the coefficients of the each component principal.

#lean_eigen<-get_eigenvalue(lean_PCA) eigenavalues which means the variance
lean_loadings<-lean_PCA$rotation # loadings
#edit(lean_loadings) edit in a square the loadings
fviz_pca_var(lean_PCA, col.var = "black")

This is variable correlation plot. X axis first principal component against Y axis second component. Negatively correlated variables there are for the first component.

Now I am going to extract the results. This function provides a list of matrices containing all the results for the active variables (coordinates, correlation between variables and axes, squared cosine and contributions)

This is the first 4 coordinates of 48 principal component. The correlation between a variable and a principal component (PC) is used as the coordinates of the variable on the PC.

var <- get_pca_var(lean_PCA)
head(var$coord)

The contributions of variables in accounting for the variability in a given principal component are expressed in percentage. 1-Variables that are correlated with PC1 and PC2 (or Dim.1 and Dim.2) are the most important in explaining the variability in the data set. 2-Variables that do not correlated with any PC or correlated with the last dimensions are variables with low contribution and might be removed to simplify the overall analysis.

head(var$contrib)

I a going to print allcontributions. It is a long list! I think it is much better for taking decision about it!

print(var)

Principal Component Analysis Results for variables
 ===================================================
  Name       Description                                    
1 "$coord"   "Coordinates for the variables"                
2 "$cor"     "Correlations between variables and dimensions"
3 "$cos2"    "Cos2 for the variables"                       
4 "$contrib" "contributions of the variables"               

Good luck sandra!plzz dont hesitate to contact me if you have any question! :-)!