motivation scale
By Levi Brackman
9/4/2017
Reading and load packages
#install.packages("foreign")#load an SPSSS file
#install.packages("psych")
#install.packages("broom")
#install.packages("gclus")
library(broom)
library(psych)
library(foreign)
library(tidyverse)## Loading tidyverse: ggplot2
## Loading tidyverse: tibble
## Loading tidyverse: tidyr
## Loading tidyverse: readr
## Loading tidyverse: purrr
## Loading tidyverse: dplyr## Conflicts with tidy packages ----------------------------------------------## %+%(): ggplot2, psych
## alpha(): ggplot2, psych
## filter(): dplyr, stats
## lag(): dplyr, statslibrary(stringr)
library(gclus)## Loading required package: clusterReading Data set
dataset = read.spss("/Users/levi.brackman/Downloads/GG T0 Motivation Scale (1).sav", to.data.frame=TRUE)View few lines of data
head(dataset, 3)## StudentID Semester t0.MvEn_1 t0.MvEn_2
## 1 2016Yr9001 Semester 2 Agree a lot - 6 Agree a lot - 6
## 2 2016Yr9003 Semester 1 Agree - 5 Agree - 5
## 3 2016Yr9003 Semester 2 Agree - 5 Agree - 5
## t0.MvEn_3 t0.MvEn_4 t0.MvEn_5
## 1 Agree a lot - 6 Agree a lot - 6 Agree a lot - 6
## 2 Agree a little - 4 Disagree a little - 3 Agree - 5
## 3 Agree - 5 Agree a little - 4 Agree a little - 4
## t0.MvEn_6 t0.MvEn_7r t0.MvEn_8r t0.MvEn_9r t0.MvEn_10r
## 1 Disagree a little - 3 1 1 1 1
## 2 Agree a little - 4 2 3 4 4
## 3 Agree - 5 3 4 4 3
## t0.MvEn_11r t0.MvEnThought_Tot t0.MvEnBeh_Tot t0.MvEnMuff_Tot
## 1 1 6.000000 5.000000 1.000000
## 2 5 4.666667 4.000000 3.000000
## 3 5 5.000000 4.333333 3.666667
## t0.MvEnGuzz_Tot
## 1 1.0
## 2 4.5
## 3 4.0There are extra characters in the colunms that R wont be able to read as well as colunms not needed for the analysis. So I now select the correct variables and remove characters from the values and save as newdataset
newdataset<-dataset %>%
select(-c(StudentID, Semester, t0.MvEnThought_Tot, t0.MvEnBeh_Tot, t0.MvEnMuff_Tot,
t0.MvEnGuzz_Tot)) %>%
mutate(t0.MvEn_1 = gsub("[^0-9]", "", t0.MvEn_1),
t0.MvEn_2 = gsub("[^0-9]", "", t0.MvEn_2),
t0.MvEn_3 = gsub("[^0-9]", "", t0.MvEn_3),
t0.MvEn_4 = gsub("[^0-9]", "", t0.MvEn_4),
t0.MvEn_5 = gsub("[^0-9]", "", t0.MvEn_5),
t0.MvEn_6 = gsub("[^0-9]", "", t0.MvEn_6),
t0.MvEn_7r = gsub("[^0-9]", "", t0.MvEn_7r),
t0.MvEn_8r = gsub("[^0-9]", "", t0.MvEn_8r),
t0.MvEn_9r = gsub("[^0-9]", "", t0.MvEn_9r),
t0.MvEn_10r = gsub("[^0-9]", "", t0.MvEn_10r),
t0.MvEn_11r = gsub("[^0-9]", "", t0.MvEn_11r))
#write_csv(newdataset, "derdataset.csv")
#names(dataset)Now view dataset again
head(newdataset, 3)## t0.MvEn_1 t0.MvEn_2 t0.MvEn_3 t0.MvEn_4 t0.MvEn_5 t0.MvEn_6 t0.MvEn_7r
## 1 6 6 6 6 6 3 1
## 2 5 5 4 3 5 4 2
## 3 5 5 5 4 4 5 3
## t0.MvEn_8r t0.MvEn_9r t0.MvEn_10r t0.MvEn_11r
## 1 1 1 1 1
## 2 3 4 4 5
## 3 4 4 3 5Colunm names have dots in them (not a good convention) so I want to rename variable without dots
newdataset<- newdataset %>% rename(MvEn_1 = t0.MvEn_1, MvEn_2 = t0.MvEn_2, MvEn_3 = t0.MvEn_3,
MvEn_4 = t0.MvEn_4, MvEn_5 = t0.MvEn_5, MvEn_6 = t0.MvEn_6,
MvEn_7r = t0.MvEn_7r, MvEn_8r = t0.MvEn_8r, MvEn_9r = t0.MvEn_9r,
MvEn_10r = t0.MvEn_10r, MvEn_11r = t0.MvEn_11r)Make all items into numeric
newdataset<- data.frame(apply(newdataset,2, as.numeric))find max inorder to reverse score items
max(newdataset$MvEn_1, na.rm = TRUE)## [1] 6Get list of variables without quotes
noquote(names(newdataset))## [1] MvEn_1 MvEn_2 MvEn_3 MvEn_4 MvEn_5 MvEn_6 MvEn_7r
## [8] MvEn_8r MvEn_9r MvEn_10r MvEn_11rReverse score columns
cols<- c("MvEn_7r", "MvEn_8r", "MvEn_9r", "MvEn_10r", "MvEn_11r")
newdataset[,cols] = lapply(cols, function(x) 6 - newdataset[, x])
#check
str(newdataset)## 'data.frame': 346 obs. of 11 variables:
## $ MvEn_1 : num 6 5 5 5 4 6 5 5 5 6 ...
## $ MvEn_2 : num 6 5 5 6 3 5 5 4 5 6 ...
## $ MvEn_3 : num 6 4 5 4 4 6 2 3 5 6 ...
## $ MvEn_4 : num 6 3 4 3 3 5 5 2 4 6 ...
## $ MvEn_5 : num 6 5 4 3 3 5 4 2 5 6 ...
## $ MvEn_6 : num 3 4 5 5 4 5 5 4 4 6 ...
## $ MvEn_7r : num 5 4 3 3 2 0 5 4 3 5 ...
## $ MvEn_8r : num 5 3 2 0 2 1 5 3 4 5 ...
## $ MvEn_9r : num 5 2 2 0 2 1 1 1 4 5 ...
## $ MvEn_10r: num 5 2 3 3 3 1 2 4 4 5 ...
## $ MvEn_11r: num 5 1 1 0 3 0 2 2 4 0 ...Correlations
The darker squares on the plot show strong correlations
#firs remove incomplete data
newdataset<- newdataset[complete.cases(newdataset[,]),]
#look at the corolations
obs<-abs(cor(newdataset))
obs## MvEn_1 MvEn_2 MvEn_3 MvEn_4 MvEn_5 MvEn_6
## MvEn_1 1.00000000 0.37941338 0.3762868 0.36680462 0.40900350 0.50961810
## MvEn_2 0.37941338 1.00000000 0.4868319 0.32994776 0.40589754 0.44848627
## MvEn_3 0.37628675 0.48683190 1.0000000 0.52939225 0.48555172 0.40617355
## MvEn_4 0.36680462 0.32994776 0.5293923 1.00000000 0.75324414 0.54633631
## MvEn_5 0.40900350 0.40589754 0.4855517 0.75324414 1.00000000 0.63413629
## MvEn_6 0.50961810 0.44848627 0.4061736 0.54633631 0.63413629 1.00000000
## MvEn_7r 0.05987714 0.08146159 0.1306251 0.18066838 0.12596689 0.08172025
## MvEn_8r 0.07838723 0.09889988 0.1093530 0.08484913 0.07685958 0.13114125
## MvEn_9r 0.34956800 0.11606995 0.0702703 0.01210666 0.03315291 0.20448360
## MvEn_10r 0.15499155 0.09247661 0.1275561 0.14758115 0.19277654 0.26231508
## MvEn_11r 0.30022373 0.19640993 0.1306738 0.14082585 0.16309319 0.35105917
## MvEn_7r MvEn_8r MvEn_9r MvEn_10r MvEn_11r
## MvEn_1 0.05987714 0.07838723 0.34956800 0.15499155 0.3002237
## MvEn_2 0.08146159 0.09889988 0.11606995 0.09247661 0.1964099
## MvEn_3 0.13062514 0.10935300 0.07027030 0.12755613 0.1306738
## MvEn_4 0.18066838 0.08484913 0.01210666 0.14758115 0.1408259
## MvEn_5 0.12596689 0.07685958 0.03315291 0.19277654 0.1630932
## MvEn_6 0.08172025 0.13114125 0.20448360 0.26231508 0.3510592
## MvEn_7r 1.00000000 0.26752603 0.12676569 0.17960163 0.2159479
## MvEn_8r 0.26752603 1.00000000 0.36954401 0.31415069 0.3854279
## MvEn_9r 0.12676569 0.36954401 1.00000000 0.46665383 0.5130856
## MvEn_10r 0.17960163 0.31415069 0.46665383 1.00000000 0.5049357
## MvEn_11r 0.21594791 0.38542795 0.51308560 0.50493567 1.0000000#soem strong corolations. Which indicate that there are items that hang well together
colors<-dmat.color(obs)
ordered<-order.single(cor(newdataset))
cpairs(newdataset, order = ordered, panel.colors = colors)
Check the factors
Parallel analysis suggests that the number of factors = 2 perhaps 3. Scree plot suggests 2. We also look at the eigenvalues: There are two components that have an eigenvalue greater than 1. According to the Keiser criterion this means two factors, at least.
parallel<-fa.parallel(newdataset, fm="ml",fa="fa") 
## Parallel analysis suggests that the number of factors = 3 and the number of components = NAparallel$fa.values## [1] 3.20741698 1.31986563 0.26388954 0.11659036 -0.01813535
## [6] -0.09772622 -0.15827505 -0.21374820 -0.30943751 -0.45869718
## [11] -0.52552008parallel2<-princomp(newdataset, cor = TRUE)
summary(parallel2)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4
## Standard deviation 1.9416218 1.4729576 0.96520913 0.91179133
## Proportion of Variance 0.3427178 0.1972367 0.08469352 0.07557849
## Cumulative Proportion 0.3427178 0.5399545 0.62464800 0.70022650
## Comp.5 Comp.6 Comp.7 Comp.8
## Standard deviation 0.85539696 0.79420330 0.74458489 0.66526095
## Proportion of Variance 0.06651854 0.05734172 0.05040061 0.04023383
## Cumulative Proportion 0.76674504 0.82408675 0.87448736 0.91472119
## Comp.9 Comp.10 Comp.11
## Standard deviation 0.61227675 0.58401667 0.47128403
## Proportion of Variance 0.03408026 0.03100686 0.02019169
## Cumulative Proportion 0.94880144 0.97980831 1.00000000plot(parallel2)##results show at least two factors
```
EFA (Exploratory Factor Analysis) & Fit indices.
Let’s now try and see what actual items make up the individual factors using EFA
Here are the fit indicies we look at:
Tucker–Lewis Index (TLI)
Comparative Fit Index (CFI)
Root Mean Squared Error of Approximation (RMSEA)
χ2 (Chi Square) test statistic (while taking into account the fact that its results are effected by the number of parameters in the model as well as the sample size)
TLI and CFI can score anywhere from 0 to 1 where results > .90 are considered an acceptable fit and > .95 represents an excellent fit to the data.
Marsh and colleagues (2010) suggest that while no golden rule exists for RMSEA, a score < .06 reflects a reasonable fit, whilst a RMSEA > .10 represents a poor fit to the data.
Two Factors
twofactor<-fa(newdataset, nfactors=2, rotate="oblimin", fm="ml")## Loading required namespace: GPArotationtwofactor## Factor Analysis using method = ml
## Call: fa(r = newdataset, nfactors = 2, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 h2 u2 com
## MvEn_1 0.45 -0.27 0.34 0.66 1.6
## MvEn_2 0.48 -0.11 0.27 0.73 1.1
## MvEn_3 0.61 -0.01 0.37 0.63 1.0
## MvEn_4 0.85 0.09 0.69 0.31 1.0
## MvEn_5 0.89 0.05 0.76 0.24 1.0
## MvEn_6 0.67 -0.22 0.58 0.42 1.2
## MvEn_7r 0.25 0.32 0.13 0.87 1.9
## MvEn_8r 0.02 0.50 0.25 0.75 1.0
## MvEn_9r 0.08 0.73 0.51 0.49 1.0
## MvEn_10r -0.07 0.61 0.40 0.60 1.0
## MvEn_11r -0.06 0.75 0.59 0.41 1.0
##
## ML1 ML2
## SS loadings 2.87 2.01
## Proportion Var 0.26 0.18
## Cumulative Var 0.26 0.44
## Proportion Explained 0.59 0.41
## Cumulative Proportion 0.59 1.00
##
## With factor correlations of
## ML1 ML2
## ML1 1.00 -0.24
## ML2 -0.24 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 55 and the objective function was 3.89 with Chi Square of 1298.49
## The degrees of freedom for the model are 34 and the objective function was 0.43
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.07
##
## The harmonic number of observations is 339 with the empirical chi square 105.47 with prob < 3e-09
## The total number of observations was 339 with Likelihood Chi Square = 142.3 with prob < 3.3e-15
##
## Tucker Lewis Index of factoring reliability = 0.859
## RMSEA index = 0.098 and the 90 % confidence intervals are 0.081 0.114
## BIC = -55.79
## Fit based upon off diagonal values = 0.97
## Measures of factor score adequacy
## ML1 ML2
## Correlation of scores with factors 0.94 0.89
## Multiple R square of scores with factors 0.89 0.79
## Minimum correlation of possible factor scores 0.78 0.59paste("CFI:", round(1-((twofactor$STATISTIC - twofactor$dof)/(twofactor$null.chisq- twofactor$null.dof)),4))## [1] "CFI: 0.9129"Three Factors
threefactor<-fa(newdataset, nfactors=3, rotate="oblimin", fm="ml")
threefactor## Factor Analysis using method = ml
## Call: fa(r = newdataset, nfactors = 3, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 ML3 h2 u2 com
## MvEn_1 0.15 -0.06 0.67 0.59 0.41 1.1
## MvEn_2 0.29 0.01 0.38 0.33 0.67 1.9
## MvEn_3 0.48 0.04 0.25 0.38 0.62 1.5
## MvEn_4 0.85 0.02 -0.02 0.71 0.29 1.0
## MvEn_5 0.89 -0.01 0.00 0.80 0.20 1.0
## MvEn_6 0.54 -0.16 0.28 0.59 0.41 1.7
## MvEn_7r 0.15 0.38 0.18 0.16 0.84 1.8
## MvEn_8r -0.05 0.56 0.12 0.28 0.72 1.1
## MvEn_9r 0.19 0.64 -0.27 0.55 0.45 1.6
## MvEn_10r -0.15 0.70 0.15 0.48 0.52 1.2
## MvEn_11r -0.03 0.71 -0.09 0.57 0.43 1.0
##
## ML1 ML2 ML3
## SS loadings 2.42 1.92 1.09
## Proportion Var 0.22 0.17 0.10
## Cumulative Var 0.22 0.39 0.49
## Proportion Explained 0.45 0.35 0.20
## Cumulative Proportion 0.45 0.80 1.00
##
## With factor correlations of
## ML1 ML2 ML3
## ML1 1.00 -0.16 0.43
## ML2 -0.16 1.00 -0.34
## ML3 0.43 -0.34 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 55 and the objective function was 3.89 with Chi Square of 1298.49
## The degrees of freedom for the model are 25 and the objective function was 0.23
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 339 with the empirical chi square 48.11 with prob < 0.0036
## The total number of observations was 339 with Likelihood Chi Square = 77.68 with prob < 2.6e-07
##
## Tucker Lewis Index of factoring reliability = 0.906
## RMSEA index = 0.08 and the 90 % confidence intervals are 0.059 0.099
## BIC = -67.97
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## ML1 ML2 ML3
## Correlation of scores with factors 0.94 0.89 0.83
## Multiple R square of scores with factors 0.89 0.79 0.69
## Minimum correlation of possible factor scores 0.78 0.59 0.39paste("CFI:", round(1-((threefactor$STATISTIC - threefactor$dof)/(threefactor$null.chisq- threefactor$null.dof)),4))## [1] "CFI: 0.9576"