── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ ggplot2::%+%() masks psych::%+%()
✖ ggplot2::alpha() masks psych::alpha()
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
new_names <-c("certain_groups_stay_in_same_place", "certain_groups_are_at_the_top_of_others", "group_equality", "everyone_equality", "no_one_right_way_to_live_life", "deft_traditional_ways", "follow_tradition", "need_a_strong_determined_leader", "tradition_show_the_best_way_to_live") #Give your variables new informative names # Update column namescolnames(data) <- new_names #Apply new names to your data frameskim(data) #Checks the variables in your data frame; evaluate for missing data
The table shows the correlation for each item measuring the concept of Social Dominance Orientation (SDO) and Right Wing Authoritarianism (RWA). 0.6 or higher are expected if variables measure the same concepts. Accordingly, for the concept of “Social Dominance Orientation,” the correlation number for variables “Group equality should be our ideal (C5_T3)” and “We should do what we can to equalize conditions for everyone (C5_T4)” is equal or higher than 0.6. For the “Right Wing Authoritarianism (RWA),” the correlation number for variables “Our country will be great if we honor the ways of our forefathers, do what the authorities tell us to do, and get rid of the “rotten apples” who are ruining everything (C5_U3)” and “What our country needs is a strong, determined leader who will crush evil and take us back to our true path(C5_U4)” is equal or higher than 0.6.
Alpha Calculation
#Calculate Cronbach's Alpha using 'psych' package##Generic format 'alpha(data, na.rm=TRUE, check.keys=TRUE) #check.keys=TRUE is important as it checks the scale direction and, if necessary, flips the order of the scale prior to running the analysis. psych::alpha(data_sdo, na.rm =TRUE, check.keys=TRUE)
The R code below calculates Cronbach’s Alpha through the psych package after using the “na.rm=TRUE” function to remove the missing data and the “check.keys=TRUE” function to flip the reverse-coded variables.
When analyzing the alpha results, “raw_alpha” and “Reliability if an item is dropped” are the two things that need to be emphasized. For “raw_alpha,” 0.7 or larger is usually considered a reliable. In addition, the “Reliability if an item is dropped” shows how alpha would change if the items are removed, which shows how well each item fits with the overall concept. The increase of “raw_alpha” shows the item is not part of the scale and might be considered to be removed from the measurement. If the “raw_alpha” goes down, it shows the item is crucial for the factor and should be kept in the measurement.
For the Social Dominance Orientation (SDO) scale, the raw_alpha is 0.63. It shows there is a space for scales to improve reliability. If removing “If certain groups stayed in their place, we would have fewer problems (C5_T1)”, the raw_alpha stays the same. If removing “It’s probably a good thing that certain groups are at the top and other groups are at the bottom (C5_T2),” the raw_alpha drops to 0.55. If removing “Group equality should be our ideal (C5_T3),” the raw_alpha drops to 0.48. If not include “We should do what we can to equalize conditions for everyone (C5_T),” the raw_alpha drops to 0.54. Accordingly, the results show that every element is essential for the scale except “If certain groups stayed in their place, we would have fewer problems (C5_T1).”
For the Right Wing Authoritarianism (RWA) scale, the raw_alpha is 0.72, which means the reliability is just right. If removing “There is no ONE right way to live life; everybody has to create their way. (C5_U1)”, the raw_alpha increased to 0.75, if not including “Our country needs free thinkers who will have the courage to defy traditional ways, even if this upsets many people. (C5_U2),” the raw_alpha dropped to 0.71. If not include “Our country will be great if we honor the ways of our forefathers, do what the authorities tell us to do, and get rid of the “rotten apples” who are ruining everything (C5_U3), ” the raw_alpha drops to 0.64. If not include “What our country really needs is a strong, determined leader who will crush evil and take us back to our true path (C5_U4),” the raw_alpha drops to 0.64. If not include “The ‘old-fashioned ways’ and ‘old-fashioned values’ still show the best way to live. (C5_U5),” the raw_alpha drops to 0.63. Accordingly, the results show that the variable “There is no ONE right way to live life; everybody has to create their own way. (C5_U1)” might be considered to be removed from the measurement.
Factor Analysis
Evaluating Correlations
cor_matrix<-cor(data_recode, use ="pairwise.complete.obs") #Saves correlation matrixcor_matrix <-round(cor_matrix, 2)cor_matrix
The correlation matrix for all the variables shows the correlation between variables to see how they relate to each other or not. It is worth noting that all variables are positively correlated. However, some variables do not significantly correlate with others. In addition, the results indicate that around four factors are measured by the variables listed above.
Screeplot
scree(data_recode)
According to the scree plot, based on the principle eigenvalues are equal and greater than one and point when the line “flattens” out, both Principal Axis Factor analysis(PAF) and Principal Component Factor analysis (PCF) show that four items might best describe the scale.
Estimate the Factor Analysis
paf_result_no_2 <-fa(data_recode, nfactors =2, rotate ="none", fm="pa") #paf modelprint(paf_result_no_2, cut =0.3) #Reports same Eigenvalues as reported in Scree Plot
Factor Analysis using method = pa
Call: fa(r = data_recode, nfactors = 2, rotate = "none", fm = "pa")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 h2 u2 com
certain_groups_stay_in_same_place_recode 0.60 0.402 0.60 1.2
certain_groups_are_at_the_top_of_others_recode 0.51 0.257 0.74 1.0
group_equality_recode 0.41 0.70 0.651 0.35 1.6
everyone_equality_recode 0.38 0.68 0.611 0.39 1.6
no_one_right_way_to_live_life_recode 0.097 0.90 1.4
deft_traditional_ways_recode 0.40 0.200 0.80 1.4
follow_tradition_recode 0.71 -0.33 0.610 0.39 1.4
need_a_strong_determined_leader_recode 0.70 0.582 0.42 1.3
tradition_show_the_best_way_to_live_recode 0.70 0.508 0.49 1.1
PA1 PA2
SS loadings 2.67 1.25
Proportion Var 0.30 0.14
Cumulative Var 0.30 0.44
Proportion Explained 0.68 0.32
Cumulative Proportion 0.68 1.00
Mean item complexity = 1.3
Test of the hypothesis that 2 factors are sufficient.
df null model = 36 with the objective function = 2.77 with Chi Square = 4519.61
df of the model are 19 and the objective function was 0.4
The root mean square of the residuals (RMSR) is 0.08
The df corrected root mean square of the residuals is 0.11
The harmonic n.obs is 1549 with the empirical chi square 651.61 with prob < 6.3e-126
The total n.obs was 1635 with Likelihood Chi Square = 659.1 with prob < 1.6e-127
Tucker Lewis Index of factoring reliability = 0.729
RMSEA index = 0.144 and the 90 % confidence intervals are 0.134 0.153
BIC = 518.51
Fit based upon off diagonal values = 0.94
Measures of factor score adequacy
PA1 PA2
Correlation of (regression) scores with factors 0.92 0.87
Multiple R square of scores with factors 0.85 0.76
Minimum correlation of possible factor scores 0.69 0.52
fa.diagram(paf_result_no_2) #Graphs the relationship
paf_result_no_4 <-fa(data_recode, nfactors =4, rotate ="none", fm="pa") #paf modelprint(paf_result_no_4,cut =0.3) #Reports same Eigenvalues as reported in Scree Plot
Factor Analysis using method = pa
Call: fa(r = data_recode, nfactors = 4, rotate = "none", fm = "pa")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 PA3 PA4 h2 u2
certain_groups_stay_in_same_place_recode 0.63 0.32 0.59 0.41
certain_groups_are_at_the_top_of_others_recode 0.55 0.39 0.53 0.47
group_equality_recode 0.40 0.67 0.67 0.33
everyone_equality_recode 0.38 0.68 0.67 0.33
no_one_right_way_to_live_life_recode 0.32 0.51 0.43 0.57
deft_traditional_ways_recode 0.46 0.50 0.55 0.45
follow_tradition_recode 0.69 -0.33 0.60 0.40
need_a_strong_determined_leader_recode 0.71 -0.32 0.68 0.32
tradition_show_the_best_way_to_live_recode 0.69 0.54 0.46
com
certain_groups_stay_in_same_place_recode 2.0
certain_groups_are_at_the_top_of_others_recode 2.3
group_equality_recode 1.9
everyone_equality_recode 1.9
no_one_right_way_to_live_life_recode 2.2
deft_traditional_ways_recode 2.6
follow_tradition_recode 1.5
need_a_strong_determined_leader_recode 1.7
tradition_show_the_best_way_to_live_recode 1.2
PA1 PA2 PA3 PA4
SS loadings 2.78 1.31 0.71 0.45
Proportion Var 0.31 0.15 0.08 0.05
Cumulative Var 0.31 0.46 0.53 0.58
Proportion Explained 0.53 0.25 0.14 0.09
Cumulative Proportion 0.53 0.78 0.91 1.00
Mean item complexity = 1.9
Test of the hypothesis that 4 factors are sufficient.
df null model = 36 with the objective function = 2.77 with Chi Square = 4519.61
df of the model are 6 and the objective function was 0.01
The root mean square of the residuals (RMSR) is 0.01
The df corrected root mean square of the residuals is 0.02
The harmonic n.obs is 1549 with the empirical chi square 5.81 with prob < 0.45
The total n.obs was 1635 with Likelihood Chi Square = 18.48 with prob < 0.0051
Tucker Lewis Index of factoring reliability = 0.983
RMSEA index = 0.036 and the 90 % confidence intervals are 0.018 0.055
BIC = -25.92
Fit based upon off diagonal values = 1
Measures of factor score adequacy
PA1 PA2 PA3 PA4
Correlation of (regression) scores with factors 0.94 0.89 0.77 0.72
Multiple R square of scores with factors 0.87 0.79 0.60 0.52
Minimum correlation of possible factor scores 0.75 0.58 0.20 0.04
fa.diagram(paf_result_no_4) #Graphs the relationship
Below are the factor analyses through PAF with different numbers of factors (2, 4) and rotation types (None, Orthogonal [varimax], and Oblique [oblimin]).
For the two-factor solution, “SS loadings” show that all two factors have eigenvalues greater than one. The proportion of the variance indicates that Factor One clearly explains 30% of the variance while Factor Two adds 14% of the explanation.
Regarding the four-factor solution, the eigenvalues of the first and second factors are greater than one, while the third and fourth factors’ eigenvalues are below one. The proportion of the variance shows that factor one explains 31% of the variance, and factor four increases by 5% of the explanation.
The next step is to measure which variables are loaded in which factors. About the two-factor solution, factor one is loaded on “Our country will be great if we honor the ways of our forefathers, do what the authorities tell us to do, and get rid of the “rotten apples” who are ruining everything (C5_U3),” “What our country really needs is a strong, determined leader who will crush evil and take us back to our true path (C5_U4),” and “The ‘old-fashioned ways’ and ‘old-fashioned values’ still show the best way to live. (C5_U5).” Factor two is loaded on “Group equality should be our ideal (C5_T3)” and “We should do what we can to equalize conditions for everyone (C5_T4).” Because the other four factors are not included, it is time to expand the number of factors when analyzing.
When moving to four-factor analysis, factor two loads the variables “Group equality should be our ideal (C5_T3)” and “We should do what we can to equalize conditions for everyone (C5_T4)” Factor three loads variables “There is no ONE right way to live life; everybody has to create their own way. (C5_U1)” and “Our country needs free thinkers who will have the courage to defy traditional ways, even if this upsets many people. (C5_U2).” Factor four loaded on “If certain groups stayed in their place, we would have fewer problems (C5_T1)” and “It’s probably a good thing that certain groups are at the top and other groups are at the bottom (C5_T2).” It is also worth noting that factor one does not have a clear factor analysis when unrotated. Thus, it is reasonable to introduce rotation to get more precise results.
Tucker-Lewis Index and the Root Mean Square Error of Approximation (RMSEA) are used to measure the fit statistics. The good fitting model for TLI is greater than or equal to 0.95, and the traditional cut-point for the RMSEA result is less than 0.05. According to the two-factor solution, the TLI is 0.729, and RMSEA is 0.08. By contrast, the TIL for the four-factor solution is 0.983, and the RMSR is 0.01 for the four-factor solution. Accordingly, the four-factor solution is better to describe the item.
The graphic below shows items that might create some latent factor.
Factor Analysis using method = pa
Call: fa(r = data_recode, nfactors = 4, rotate = "varimax", fm = "pa")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 PA4 PA3 h2 u2
certain_groups_stay_in_same_place_recode 0.39 0.66 0.59 0.41
certain_groups_are_at_the_top_of_others_recode 0.68 0.53 0.47
group_equality_recode 0.79 0.67 0.33
everyone_equality_recode 0.81 0.67 0.33
no_one_right_way_to_live_life_recode 0.64 0.43 0.57
deft_traditional_ways_recode 0.69 0.55 0.45
follow_tradition_recode 0.72 0.60 0.40
need_a_strong_determined_leader_recode 0.80 0.68 0.32
tradition_show_the_best_way_to_live_recode 0.67 0.54 0.46
com
certain_groups_stay_in_same_place_recode 1.7
certain_groups_are_at_the_top_of_others_recode 1.3
group_equality_recode 1.1
everyone_equality_recode 1.1
no_one_right_way_to_live_life_recode 1.1
deft_traditional_ways_recode 1.3
follow_tradition_recode 1.3
need_a_strong_determined_leader_recode 1.1
tradition_show_the_best_way_to_live_recode 1.5
PA1 PA2 PA4 PA3
SS loadings 1.83 1.37 1.06 0.99
Proportion Var 0.20 0.15 0.12 0.11
Cumulative Var 0.20 0.36 0.47 0.58
Proportion Explained 0.35 0.26 0.20 0.19
Cumulative Proportion 0.35 0.61 0.81 1.00
Mean item complexity = 1.3
Test of the hypothesis that 4 factors are sufficient.
df null model = 36 with the objective function = 2.77 with Chi Square = 4519.61
df of the model are 6 and the objective function was 0.01
The root mean square of the residuals (RMSR) is 0.01
The df corrected root mean square of the residuals is 0.02
The harmonic n.obs is 1549 with the empirical chi square 5.81 with prob < 0.45
The total n.obs was 1635 with Likelihood Chi Square = 18.48 with prob < 0.0051
Tucker Lewis Index of factoring reliability = 0.983
RMSEA index = 0.036 and the 90 % confidence intervals are 0.018 0.055
BIC = -25.92
Fit based upon off diagonal values = 1
Measures of factor score adequacy
PA1 PA2 PA4 PA3
Correlation of (regression) scores with factors 0.87 0.89 0.78 0.79
Multiple R square of scores with factors 0.76 0.78 0.61 0.62
Minimum correlation of possible factor scores 0.53 0.57 0.23 0.24
fa.diagram(paf_result_var_4) #Graphs the relationship
Factor Analysis using method = pa
Call: fa(r = data_recode, nfactors = 4, rotate = "oblimin", fm = "pa")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 PA4 PA3 h2
certain_groups_stay_in_same_place_recode 0.68 0.59
certain_groups_are_at_the_top_of_others_recode 0.74 0.53
group_equality_recode 0.80 0.67
everyone_equality_recode 0.82 0.67
no_one_right_way_to_live_life_recode 0.68 0.43
deft_traditional_ways_recode 0.70 0.55
follow_tradition_recode 0.71 0.60
need_a_strong_determined_leader_recode 0.85 0.68
tradition_show_the_best_way_to_live_recode 0.68 0.54
u2 com
certain_groups_stay_in_same_place_recode 0.41 1.1
certain_groups_are_at_the_top_of_others_recode 0.47 1.0
group_equality_recode 0.33 1.0
everyone_equality_recode 0.33 1.0
no_one_right_way_to_live_life_recode 0.57 1.0
deft_traditional_ways_recode 0.45 1.0
follow_tradition_recode 0.40 1.1
need_a_strong_determined_leader_recode 0.32 1.0
tradition_show_the_best_way_to_live_recode 0.46 1.1
PA1 PA2 PA4 PA3
SS loadings 1.80 1.37 1.10 1.00
Proportion Var 0.20 0.15 0.12 0.11
Cumulative Var 0.20 0.35 0.47 0.58
Proportion Explained 0.34 0.26 0.21 0.19
Cumulative Proportion 0.34 0.60 0.81 1.00
With factor correlations of
PA1 PA2 PA4 PA3
PA1 1.00 0.14 0.59 0.33
PA2 0.14 1.00 0.21 0.33
PA4 0.59 0.21 1.00 0.23
PA3 0.33 0.33 0.23 1.00
Mean item complexity = 1
Test of the hypothesis that 4 factors are sufficient.
df null model = 36 with the objective function = 2.77 with Chi Square = 4519.61
df of the model are 6 and the objective function was 0.01
The root mean square of the residuals (RMSR) is 0.01
The df corrected root mean square of the residuals is 0.02
The harmonic n.obs is 1549 with the empirical chi square 5.81 with prob < 0.45
The total n.obs was 1635 with Likelihood Chi Square = 18.48 with prob < 0.0051
Tucker Lewis Index of factoring reliability = 0.983
RMSEA index = 0.036 and the 90 % confidence intervals are 0.018 0.055
BIC = -25.92
Fit based upon off diagonal values = 1
Measures of factor score adequacy
PA1 PA2 PA4 PA3
Correlation of (regression) scores with factors 0.91 0.90 0.86 0.83
Multiple R square of scores with factors 0.84 0.81 0.74 0.68
Minimum correlation of possible factor scores 0.67 0.61 0.48 0.36
fa.diagram(paf_result_obl_4) #Graphs the relationship
After adding the orthogonal and oblique rotation, the value for “SS loadings” is close to eigenvalues equal to or greater than one, like “1.80 1.37 1.10 1.00” for oblique rotation. The proportion variance does not have huge differences, such as “0.20 0.15 0.12 0.11” for oblique rotation. It shows rotations are effectively displaying the pattern more clearly. It is also interesting to discover that oblique rotation performs better on eigenvalues and variances than orthogonal rotation.
Comparing PCF and PAF Approaches
The analysis below uses the PCF approach with no rotation, orthogonal rotation, and oblique rotation.
pcf_result_no_4 <-principal(data_recode, nfactors =4, rotate ="none") #PCF approach with no rotationprint (pcf_result_no_4, cut =0.3) #Reports same Eigenvalues as reported in Scree Plot
Principal Components Analysis
Call: principal(r = data_recode, nfactors = 4, rotate = "none")
Standardized loadings (pattern matrix) based upon correlation matrix
PC1 PC2 PC3 PC4 h2 u2
certain_groups_stay_in_same_place_recode 0.68 0.40 0.74 0.26
certain_groups_are_at_the_top_of_others_recode 0.60 -0.33 0.59 0.83 0.17
group_equality_recode 0.42 0.72 -0.35 0.82 0.18
everyone_equality_recode 0.40 0.73 -0.33 0.83 0.17
no_one_right_way_to_live_life_recode 0.37 0.31 0.71 0.78 0.22
deft_traditional_ways_recode 0.50 0.38 0.56 0.71 0.29
follow_tradition_recode 0.73 -0.38 0.73 0.27
need_a_strong_determined_leader_recode 0.73 -0.35 -0.33 0.77 0.23
tradition_show_the_best_way_to_live_recode 0.76 -0.34 0.71 0.29
com
certain_groups_stay_in_same_place_recode 2.2
certain_groups_are_at_the_top_of_others_recode 2.6
group_equality_recode 2.1
everyone_equality_recode 2.1
no_one_right_way_to_live_life_recode 2.2
deft_traditional_ways_recode 2.8
follow_tradition_recode 1.7
need_a_strong_determined_leader_recode 1.9
tradition_show_the_best_way_to_live_recode 1.5
PC1 PC2 PC3 PC4
SS loadings 3.19 1.67 1.19 0.88
Proportion Var 0.35 0.19 0.13 0.10
Cumulative Var 0.35 0.54 0.67 0.77
Proportion Explained 0.46 0.24 0.17 0.13
Cumulative Proportion 0.46 0.70 0.87 1.00
Mean item complexity = 2.1
Test of the hypothesis that 4 components are sufficient.
The root mean square of the residuals (RMSR) is 0.07
with the empirical chi square 625.62 with prob < 6.9e-132
Fit based upon off diagonal values = 0.95
fa.diagram(pcf_result_no_4) #Graphs the relationship
pcf_result_var_4 <-principal(data_recode,nfactors =4, rotate ="varimax") #PCF approach with varimax rotationprint (pcf_result_var_4, cut =0.3) #Rotation reveals cleaner factors that are obscured
Principal Components Analysis
Call: principal(r = data_recode, nfactors = 4, rotate = "varimax")
Standardized loadings (pattern matrix) based upon correlation matrix
RC1 RC2 RC4 RC3 h2 u2
certain_groups_stay_in_same_place_recode 0.39 0.76 0.74 0.26
certain_groups_are_at_the_top_of_others_recode 0.89 0.83 0.17
group_equality_recode 0.89 0.82 0.18
everyone_equality_recode 0.90 0.83 0.17
no_one_right_way_to_live_life_recode 0.88 0.78 0.22
deft_traditional_ways_recode 0.80 0.71 0.29
follow_tradition_recode 0.81 0.73 0.27
need_a_strong_determined_leader_recode 0.86 0.77 0.23
tradition_show_the_best_way_to_live_recode 0.80 0.71 0.29
com
certain_groups_stay_in_same_place_recode 1.5
certain_groups_are_at_the_top_of_others_recode 1.1
group_equality_recode 1.1
everyone_equality_recode 1.0
no_one_right_way_to_live_life_recode 1.0
deft_traditional_ways_recode 1.2
follow_tradition_recode 1.2
need_a_strong_determined_leader_recode 1.1
tradition_show_the_best_way_to_live_recode 1.2
RC1 RC2 RC4 RC3
SS loadings 2.24 1.71 1.50 1.48
Proportion Var 0.25 0.19 0.17 0.16
Cumulative Var 0.25 0.44 0.61 0.77
Proportion Explained 0.32 0.25 0.22 0.21
Cumulative Proportion 0.32 0.57 0.79 1.00
Mean item complexity = 1.2
Test of the hypothesis that 4 components are sufficient.
The root mean square of the residuals (RMSR) is 0.07
with the empirical chi square 625.62 with prob < 6.9e-132
Fit based upon off diagonal values = 0.95
fa.diagram(pcf_result_var_4)
pcf_result_obl_4 <-principal(data_recode,nfactors =4, rotate ="oblimin") #PCF approach with oblimin rotationprint (pcf_result_obl_4, cut =0.3) #Rotation reveals cleaner factors that are obscured
Principal Components Analysis
Call: principal(r = data_recode, nfactors = 4, rotate = "oblimin")
Standardized loadings (pattern matrix) based upon correlation matrix
TC1 TC2 TC3 TC4 h2
certain_groups_stay_in_same_place_recode 0.75 0.74
certain_groups_are_at_the_top_of_others_recode 0.93 0.83
group_equality_recode 0.89 0.82
everyone_equality_recode 0.91 0.83
no_one_right_way_to_live_life_recode 0.91 0.78
deft_traditional_ways_recode 0.79 0.71
follow_tradition_recode 0.81 0.73
need_a_strong_determined_leader_recode 0.89 0.77
tradition_show_the_best_way_to_live_recode 0.82 0.71
u2 com
certain_groups_stay_in_same_place_recode 0.26 1.2
certain_groups_are_at_the_top_of_others_recode 0.17 1.0
group_equality_recode 0.18 1.0
everyone_equality_recode 0.17 1.0
no_one_right_way_to_live_life_recode 0.22 1.0
deft_traditional_ways_recode 0.29 1.1
follow_tradition_recode 0.27 1.1
need_a_strong_determined_leader_recode 0.23 1.0
tradition_show_the_best_way_to_live_recode 0.29 1.1
TC1 TC2 TC3 TC4
SS loadings 2.25 1.71 1.48 1.51
Proportion Var 0.25 0.19 0.16 0.17
Cumulative Var 0.25 0.44 0.60 0.77
Proportion Explained 0.32 0.25 0.21 0.22
Cumulative Proportion 0.32 0.57 0.78 1.00
With component correlations of
TC1 TC2 TC3 TC4
TC1 1.00 0.12 0.23 0.42
TC2 0.12 1.00 0.21 0.16
TC3 0.23 0.21 1.00 0.14
TC4 0.42 0.16 0.14 1.00
Mean item complexity = 1.1
Test of the hypothesis that 4 components are sufficient.
The root mean square of the residuals (RMSR) is 0.07
with the empirical chi square 625.62 with prob < 6.9e-132
Fit based upon off diagonal values = 0.95
fa.diagram(pcf_result_obl_4)
After comparing the “ss loadings” and proportion of variances for PAF and PCF when no rotation, orthogonal rotation, and oblique rotation, it seems that the PCF performs better because the number of “ss loadings” is higher, and the number of proportion variance is close to each other. However, it is also worth noting that the RMSR for the PCF approach is all over 0.05.
In conclusion, the method used for analysis might be the PAF approach with orthogonal rotation.
Conclusion For Factor Analysis
According to the analysis above, the eigenvalues for each factor would be: Factor one: 1.8, Factor two: 1.37, Factor three: 1.00, Factor four: 1.10
According to the graphic PAF approach with Orthogonal rotation, the first potential factor is established by “Our country will be great if we honor the ways of our forefathers, do what the authorities tell us to do, and get rid of the “rotten apples” who are ruining everything (C5_U3)” “What our country really needs is a strong, determined leader who will crush evil and take us back to our true path (C5_U4)” and “The ‘old-fashioned ways’ and ‘old-fashioned values’ still show the best way to live. (C5_U5)” It could be named “Approve Right Wing Authoritarianism.” The second factor contains elements “Group equality should be our ideal (C5_T3)” and “We should do what we can to equalize conditions for everyone (C5_T4)” The name for this factor will be “Disapprove Social Dominance Orientation (SDO).” The third factor involves “If certain groups stayed in their place, we would have fewer problems (C5_T1)” and It’s probably a good thing that certain groups are at the top and other groups are at the bottom (C5_T2)” It is named “Approve Social Dominance Orientation (SDO).” The fourth factor would be “There is no ONE right way to live life; everybody has to create their own way. (C5_U1)” and “Our country needs free thinkers who will have the courage to defy traditional ways, even if this upsets many people. (C5_U2)” . It is called “Disapprove Right Wing Authoritarianism.”
About Latent Concept
In conclusion, Social Dominance Orientation and Right Wing Authoritarianism measure different underlying concepts as there are no one variables that intersect to target a potential concept. Besides, it will make measurement more precise when having subdivisions of “approval” and “disapproval.” The latent concepts listed in the “Conclusion For Factor Analysis” section also show each scale is multidimensional rather than one-dimensional. In addition, various variables measure the front and back sides of each concept, which also creates potential concepts.
In addition, in the graphic for factor analysis, it is interesting to find that “Approve Right Wing Authoritarianism” and “Approve Social Dominance Orientation (SDO)” have some correlation (0.6) as they both somewhat mention authority, hierarchy, and some traditional belief.
New Variables
#With the new variables coded in same direction, we create the new scale 'racial_resent'data_recode <- data_recode %>%mutate(sdo_disapprove= (group_equality_recode+ everyone_equality_recode) /2) #Add across individual items and divide by the total number of items. Note this uses casewise deletion so any case that did not answer each question is removed from the calculation summary(data_recode$sdo_disapprove) #Examine the
Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
1.000 2.000 3.000 2.796 3.500 5.000 84
# Calculate the correlation matrixcor_matrix_sdo_new <-cor(data_sdo_new, use ="complete.obs") #Note "complete.obs" removes any case with a NA value # View the correlation matrixprint(cor_matrix_sdo_new)
The new variable measures the “Disapprove Social Dominance Orientation (SDO).” According to the correlation between new variables and other original variables, the new variables are highly correlated with the two original variables, “Group equality should be our ideal (C5_T3)” and “We should do what we can to equalize conditions for everyone (C5_T4).” (The numbers are 0.9012425 and 0.92222262.”)
Reference:
“Cronbach’s Alpha” by Dr. CEStapleton https://rpubs.com/DACSS_Prof/1271415
“Factor Analysis Tutorial Using Political Emotions” by Dr. CEStapleton https://rpubs.com/DACSS_Prof/1271348
