FILEPATH='~/Downloads/School Survey(1-14).xls'
SS <- read_excel(FILEPATH)
names(SS) <- c( "ID", "Start_time","Completion_time","Email","Name",
"Year_Level","Email_2","Postal_Code","Accessibility",
"Achievement_Results","Teaching_Experience","Teacher_Friendly",
"Facilities_Maintanance","Teacher_Additional", "Student_Behaviour",
"Facilities","Personal_Effort","Parental_Influence",
"Other_Engagement", "Peer_friend","School_Experience","Recommendation"
)
SS2 = subset(SS,
select = -c(ID, Name, Email, Postal_Code, Year_Level,Email_2, Start_time, Completion_time))
SS2.1 = subset(SS, select = -c(Start_time, Completion_time, Email, Name) )
summary(SS2.1)
## ID Year_Level Email_2 Postal_Code
## Min. : 1.0 Length:63 Length:63 Length:63
## 1st Qu.:16.5 Class :character Class :character Class :character
## Median :32.0 Mode :character Mode :character Mode :character
## Mean :32.0
## 3rd Qu.:47.5
## Max. :63.0
## Accessibility Achievement_Results Teaching_Experience Teacher_Friendly
## Min. : 1.000 Min. : 1.000 Min. : 1.00 Min. : 1.000
## 1st Qu.: 7.000 1st Qu.: 6.000 1st Qu.: 7.00 1st Qu.: 7.000
## Median : 8.000 Median : 7.000 Median : 7.00 Median : 8.000
## Mean : 7.968 Mean : 7.032 Mean : 7.27 Mean : 8.032
## 3rd Qu.:10.000 3rd Qu.: 8.000 3rd Qu.: 8.00 3rd Qu.:10.000
## Max. :10.000 Max. :10.000 Max. :10.00 Max. :10.000
## Facilities_Maintanance Teacher_Additional Student_Behaviour Facilities
## Min. : 1.000 Min. : 1.000 Min. : 1.000 Min. : 1.000
## 1st Qu.: 5.000 1st Qu.: 7.000 1st Qu.: 5.500 1st Qu.: 5.000
## Median : 6.000 Median : 8.000 Median : 6.000 Median : 7.000
## Mean : 6.365 Mean : 8.048 Mean : 6.444 Mean : 6.587
## 3rd Qu.: 8.000 3rd Qu.: 9.500 3rd Qu.: 8.000 3rd Qu.: 8.000
## Max. :10.000 Max. :10.000 Max. :10.000 Max. :10.000
## Personal_Effort Parental_Influence Other_Engagement Peer_friend
## Min. : 1.000 Min. : 1.000 Min. : 2.000 Min. : 3.00
## 1st Qu.: 7.000 1st Qu.: 6.000 1st Qu.: 6.000 1st Qu.: 7.00
## Median : 8.000 Median : 7.000 Median : 7.000 Median : 9.00
## Mean : 7.952 Mean : 7.159 Mean : 6.746 Mean : 8.46
## 3rd Qu.: 9.000 3rd Qu.: 9.000 3rd Qu.: 8.000 3rd Qu.:10.00
## Max. :10.000 Max. :10.000 Max. :10.000 Max. :10.00
## School_Experience Recommendation
## Min. : 1.000 Min. : 1.000
## 1st Qu.: 7.000 1st Qu.: 6.500
## Median : 8.000 Median : 8.000
## Mean : 7.746 Mean : 7.587
## 3rd Qu.: 9.000 3rd Qu.:10.000
## Max. :10.000 Max. :10.000
SS2$School_Experience=as.numeric(SS2$School_Experience)
SS2$Recommendation=as.numeric(SS2$Recommendation)
cormatrix <- cor(SS2)
ggcorrplot(cormatrix)
KMO(cormatrix)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = cormatrix)
## Overall MSA = 0.8
## MSA for each item =
## Accessibility Achievement_Results Teaching_Experience
## 0.76 0.86 0.87
## Teacher_Friendly Facilities_Maintanance Teacher_Additional
## 0.94 0.81 0.80
## Student_Behaviour Facilities Personal_Effort
## 0.79 0.85 0.77
## Parental_Influence Other_Engagement Peer_friend
## 0.48 0.71 0.79
## School_Experience Recommendation
## 0.78 0.78
parallel <- fa.parallel(cormatrix, fm = 'minres', fa = 'fa')
## Parallel analysis suggests that the number of factors = 3 and the number of components = NA
nfac <- fa(SS2, nfactors = 5, rotate = "varimax",fm="minres")
nfac
## Factor Analysis using method = minres
## Call: fa(r = SS2, nfactors = 5, rotate = "varimax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR3 MR2 MR5 MR4 h2 u2 com
## Accessibility 0.74 0.04 0.16 0.12 -0.17 0.62 0.385 1.3
## Achievement_Results 0.62 0.31 0.35 0.12 0.03 0.63 0.373 2.2
## Teaching_Experience 0.38 0.60 0.16 0.21 0.09 0.59 0.414 2.2
## Teacher_Friendly 0.48 0.36 0.33 0.27 0.00 0.55 0.450 3.4
## Facilities_Maintanance 0.12 0.79 0.20 0.06 0.00 0.68 0.315 1.2
## Teacher_Additional 0.42 0.39 0.04 0.30 -0.03 0.43 0.575 2.8
## Student_Behaviour 0.39 0.26 0.35 0.60 -0.09 0.71 0.291 2.9
## Facilities 0.15 0.74 0.22 0.10 -0.01 0.63 0.366 1.3
## Personal_Effort 0.81 0.28 0.00 0.23 0.29 0.86 0.139 1.7
## Parental_Influence -0.01 0.00 0.15 0.07 0.82 0.70 0.296 1.1
## Other_Engagement 0.19 0.18 0.18 0.93 0.20 1.00 0.002 1.3
## Peer_friend 0.19 0.03 0.45 0.50 0.00 0.49 0.506 2.3
## School_Experience 0.23 0.32 0.83 0.19 0.14 0.91 0.093 1.6
## Recommendation 0.11 0.33 0.77 0.29 0.20 0.84 0.157 1.9
##
## MR1 MR3 MR2 MR5 MR4
## SS loadings 2.47 2.32 2.04 1.90 0.91
## Proportion Var 0.18 0.17 0.15 0.14 0.06
## Cumulative Var 0.18 0.34 0.49 0.62 0.69
## Proportion Explained 0.26 0.24 0.21 0.20 0.09
## Cumulative Proportion 0.26 0.50 0.71 0.91 1.00
##
## Mean item complexity = 2
## Test of the hypothesis that 5 factors are sufficient.
##
## The degrees of freedom for the null model are 91 and the objective function was 9.07 with Chi Square of 512.63
## The degrees of freedom for the model are 31 and the objective function was 0.78
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 63 with the empirical chi square 10.28 with prob < 1
## The total number of observations was 63 with Likelihood Chi Square = 41.22 with prob < 0.1
##
## Tucker Lewis Index of factoring reliability = 0.923
## RMSEA index = 0.071 and the 90 % confidence intervals are 0 0.127
## BIC = -87.22
## Fit based upon off diagonal values = 1
print(nfac$loadings, cutoff = 0.4)
##
## Loadings:
## MR1 MR3 MR2 MR5 MR4
## Accessibility 0.737
## Achievement_Results 0.624
## Teaching_Experience 0.601
## Teacher_Friendly 0.483
## Facilities_Maintanance 0.790
## Teacher_Additional 0.421
## Student_Behaviour 0.600
## Facilities 0.745
## Personal_Effort 0.805
## Parental_Influence 0.822
## Other_Engagement 0.925
## Peer_friend 0.449 0.504
## School_Experience 0.834
## Recommendation 0.770
##
## MR1 MR3 MR2 MR5 MR4
## SS loadings 2.469 2.320 2.041 1.902 0.907
## Proportion Var 0.176 0.166 0.146 0.136 0.065
## Cumulative Var 0.176 0.342 0.488 0.624 0.688
SS3 = subset(SS2, select = -c(Teaching_Experience, Teacher_Additional, Recommendation, Peer_friend, Student_Behaviour, Teacher_Friendly) )
nfac <- fa(SS3, nfactors = 5, rotate = "varimax",fm="minres")
nfac
## Factor Analysis using method = minres
## Call: fa(r = SS3, nfactors = 5, rotate = "varimax", fm = "minres")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 MR4 MR5 h2 u2 com
## Accessibility 0.79 0.05 -0.22 0.22 0.11 0.74 0.262 1.4
## Achievement_Results 0.62 0.31 0.07 0.34 0.05 0.60 0.403 2.1
## Facilities_Maintanance 0.15 0.82 0.03 0.13 0.03 0.72 0.283 1.1
## Facilities 0.17 0.76 0.01 0.17 0.16 0.67 0.335 1.3
## Personal_Effort 0.86 0.26 0.37 -0.11 0.19 0.99 0.015 1.7
## Parental_Influence 0.00 -0.01 0.65 0.10 0.09 0.44 0.560 1.1
## Other_Engagement 0.30 0.22 0.30 0.19 0.46 0.47 0.526 3.5
## School_Experience 0.25 0.39 0.26 0.70 0.17 0.81 0.192 2.3
##
## MR1 MR2 MR3 MR4 MR5
## SS loadings 1.94 1.63 0.77 0.76 0.33
## Proportion Var 0.24 0.20 0.10 0.10 0.04
## Cumulative Var 0.24 0.45 0.54 0.64 0.68
## Proportion Explained 0.36 0.30 0.14 0.14 0.06
## Cumulative Proportion 0.36 0.66 0.80 0.94 1.00
##
## Mean item complexity = 1.8
## Test of the hypothesis that 5 factors are sufficient.
##
## The degrees of freedom for the null model are 28 and the objective function was 3.11 with Chi Square of 181.66
## The degrees of freedom for the model are -2 and the objective function was 0
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is NA
##
## The harmonic number of observations is 63 with the empirical chi square 0 with prob < NA
## The total number of observations was 63 with Likelihood Chi Square = 0 with prob < NA
##
## Tucker Lewis Index of factoring reliability = 1.195
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## MR1 MR2 MR3 MR4 MR5
## Correlation of (regression) scores with factors 0.95 0.88 0.82 0.87 0.50
## Multiple R square of scores with factors 0.90 0.78 0.67 0.75 0.25
## Minimum correlation of possible factor scores 0.81 0.56 0.35 0.50 -0.51
print(nfac$loadings, cutoff = 0.4)
##
## Loadings:
## MR1 MR2 MR3 MR4 MR5
## Accessibility 0.790
## Achievement_Results 0.616
## Facilities_Maintanance 0.822
## Facilities 0.764
## Personal_Effort 0.857
## Parental_Influence 0.649
## Other_Engagement 0.460
## School_Experience 0.704
##
## MR1 MR2 MR3 MR4 MR5
## SS loadings 1.936 1.626 0.771 0.764 0.326
## Proportion Var 0.242 0.203 0.096 0.095 0.041
## Cumulative Var 0.242 0.445 0.542 0.637 0.678
MRw=nfac$weights
MR1w=nfac$weights[,1]
MR2w=nfac$weights[,2]
MR3w=nfac$weights[,3]
MR4w=nfac$weights[,4]
MR5w=nfac$weights[,5]
dim(SS3)
## [1] 63 8
dim(MRw)
## [1] 8 5
SS4= data.matrix(SS3) %*% data.matrix(MRw)
dim(SS4)
## [1] 63 5
SS5=as.data.frame(SS4)
SS5$Satis=SS$Recommendation
reg <- lm( SS5$Satis ~ SS5$MR1 + SS5$MR2 + SS5$MR3 + SS5$MR4 + SS5$MR5, data = SS5)
coefficients <- as.data.frame(reg$coefficients)
colnames(coefficients) <- 'coefficients'
summary(reg)
##
## Call:
## lm(formula = SS5$Satis ~ SS5$MR1 + SS5$MR2 + SS5$MR3 + SS5$MR4 +
## SS5$MR5, data = SS5)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.63590 -0.63813 -0.02759 0.73685 2.97328
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.72314 0.86035 -2.003 0.0500 *
## SS5$MR1 0.12934 0.09053 1.429 0.1585
## SS5$MR2 0.45761 0.07856 5.825 2.78e-07 ***
## SS5$MR3 0.45393 0.09640 4.709 1.64e-05 ***
## SS5$MR4 0.93928 0.09568 9.816 7.38e-14 ***
## SS5$MR5 0.36233 0.18046 2.008 0.0494 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.189 on 57 degrees of freedom
## Multiple R-squared: 0.768, Adjusted R-squared: 0.7476
## F-statistic: 37.73 on 5 and 57 DF, p-value: < 2.2e-16