Module Project: Factor Analysis of Personality Data Performing the Factor Analysis, Methodology, and Results

Module Project: Factor Analysis of Personality Data

Performing the Factor Analysis, Methodology, and Results

 

Name: Jimmy Petruzzi

MSC Mental health psychology  LPSY-302-5

LPSY 316: Personality, Individual Differences, and Intelligence

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

METHOD

 

Participants:

Participants included 1006 people aged from 9 years of age to 12 years of age. Equal distribution of male and females, residing in the Nunavut state in  Canada. In accordance to the Canada School of Public Service Act, primary and secondary school attendance in Nunavut state is compulsory, part of the selection criteria was based on levels of school attendance. Participants were excluded if they had above unauthorised absenteeism above legal school attendance.

Participants parents and caregivers  were requested to   provide information on employment status in order for the questionnaire participation to reflect society to increase  social validity.

Design

In designing the questionnaire we took into consideration the variable factors   which can impact the reliability of a participation response, factors such as interpretation of the question, the participants cognitive ability and motivation during the test.

The following research Gurven, Rueden, Massenkoff,Kaplan, Vie,(2013) indicated limitations of the FFM when administered amongst a rural community in Bolivia, the questionnaire was translated, though it appeared literacy was amongst the correlating factors impacting the reliability of the questionnaire, the significance  of this research was the FFM has been demonstrated to be more reliable in developed nations, whilst this is not a direct  correlating factor amongst our participants in the Intuit community  it did suggest taking  this and previous research into consideration  about adapting the FFM  for  the adolescents participants.

We produced a modified sample questionnaire, parent or carer consent was authorised to conduct   an initial modified version of the questionnaire.  The questionnaire was trialled amongst 124 participants, equal distribution of male and female, the age ranges between 9 years of age to 12 year of age. Upon modification  and administration  of the  modified  Questionnaire and an evaluation of the data. A 25-item questionnaire, Costa and McCrae (1992) was developed to measure the Big Five personality factors in Inuit children in Canada.

Five items were taken  from each of the five IPIP scales that measure the Big Five personality factors, adapting them where necessary so that they would be relevant to the lives and cognitive abilities of 9-year-old to 12-year-old Inuit children and translating them into the Inuktitut language.

Materials:

Using the FFM Inventory developed by Costa and McCrae (1992), as a platform to develop  a  25- Item questionnaire procured  from  the IPIP,  utilising  a five point  Likert scale.

The participants completed the questionnaire with paper and black pen, SPSS program and software was used to   implement   the, Factor Analysis and PCA, the parallel analysis implemented with the e O’Connor learning resource

Procedure:

Informed consent was compulsory from parents and caregivers of the participants as the participants age range was 9 years of age to 12 years of age. The questionnaire was administered to the participants on the 23rd of June 2018 at 930am on commencement of the morning classroom lesson, the test was conducted in the school classrooms and the young people remained anonymous. The participants were instructed not to discuss questions with other participants, any questions could be discussed with study supervisors which could also speak intuit language

The duration for completion of the questionnaire, was in line with the duration of the compulsory education morning framework in Canada, which is approx. 2 hours and 30 minutes, as the questionnaire was designated during academic term time, minimal disruption to designated lesson, students returned to the usual class on completion.

The content of the questionnaire was the same for all participants, research by  Goldberg (2001) suggests the FFM can be adapted successfully  for the administration to suit the cognitive abilities of the participant’s, in accordance and consideration of research by Goldberg (2001) the questionnaire was adapted to suit the cognitive abilities of the participants and translated  from English into Intuit language to ensure  increased validity and reliability in measurements.

 

 

 

 

 

 

 

 

Results

The object of the PCA was to Identify the eigenvalues, there after utilizing the eigenvalues  to conduct  a scree test.  We also conducted  the Kaiser-Guttman test to define the  number of factors, although we were uncertain about the accuracy of the data. We proceeded in  utilizing  the O’Connor resource and conducted a parallel analysis ( which can be referred to in the  appendix)

Once we identified the number of factors using the  O’Connor resource, based on the number of factors we had discovered in our data, we were able to conduct a Factor Analysis with Oblique Rotation using oblimin  utilising SPSS software ( the SPSS data can be referred to in the appendix)

Having conducted the PCA, the data indicated the first 6 components having an eigenvalue > 1.0.

The Mean eigenvalues we identified as 1.297, 1.252, 1.217, 1.189, 1.163, 1.137 see Table 2: below

Extraction Method: Principal Component Analysis.

Factor Critical value eigenvalue Variance % Cumulative %
1 1.297 2.160 8.641 8.641
2 1.252 2.114 8.456 17.098
3 1.221 1.893 7.571 24.668
4 1.189 1.703 6.810 31.478
5 1.163 1.642 6.569 38.047
6 1.137 1.064 4.258 42.305
         

Table 2: Parallel-test of Eigenvalues

Having identified the list of eigenvalues we performed a scree test.

Figure-02: Scree-plot of unrotated PCA-test (please see index for scree plot diagram )

According to Field (2013) the inflection point of retaining factors is above the curve which can be identified on the Scree plot graph. The point of inflexion is where the slope of the line changes dramatically, our findings demonstrated  six factor-items loading  at point of inflection at component 7,  amongst components of the IPIP-25-item questionnaire  2.160,2.114,1.893,1.703,1.642  please see Table-03:

According to Stevens (2002) the Scree plot is relatively reliable in providing data for factor selection in samples of 200 participants or more, we had 1006 sample so we were confident in our data collected factor selection.

Rotated Principle analysis

Initial eigenvalues                                                      Loadings rotations

Factor total cumulative% total cumulative% total
1 2.160 8.641 1.411 5.642 1.375
2 2.114 17.098 1.370 11.121 1.359
3 1.893 24.668 1.131 15.647 1.100
4 1.703 31.478 .960 19.487 1.054
5 1.642 38.047 .866 22.952 .878
           
           

Table-03: PAF- Analysis test results

The factor rotation technique was used to differentiate between factors to interpret factor variable low and high loading with reliable extraction of data.

Upon establishing the data we ran a unrotated PCA to assist us in omitting the number of factor loads from the IPIP- 25 item questionnaire.

According to Horn (1965) we retain the factors that are higher from the research data, than the corresponding data which is run randomly.

Research by Fabrigar, & Wegener,(2012) was significant in our decision to utilised an oblique rotation method, we were able to identify the highest factor loadings see Figure 4:

According to  Cooper (2010), if we  use an oblique rotation, we should analyse the  Pattern matrix a table ( please see index)  the table enabled us to identify the factor for each item which has the highest loadings The items we analysed had correlations of  .4 and  higher, If they are related to each other, this means there are factors underlying the items and data.

 

 

 

 

 

Factor Analysis with Oblique Rotation

Factor            
1:  Conscientiousness 2 (.524) 13 (-507) 17 (.506) 19 (.543) 22 (.519)  
2:  Neuroticism 5 (.430) 8 (.520) 11 (.492) 16 (.507) 24 (.476) 15 (-.407)
3: Extroversion 4 (.385) 6 (-.520) 14 (.476) 20(.404) 25 (.524)  
4: openness 3(.535) 10 (.552) 23 (.508) 21 (.423)    
5:agreeableness 1 (.448) 7(.448) 12 (.408) 18 (.535)    
             

Figure 4: Relationships between factors

We identified that 25 items questionnaire had successfully measured, by the five factors we expected. After analysing the results we were able to determine, factor 1 Conscientiousness  had a correlation  With 2 ,13 ,17 ,19 ,22,  Factor 2 neuroticism  had a correlation with 5,8,11,16,24,15 ,Factor 3 had a correlation with 4,6 ,14,20,25 ,Factor 4  openness had a correlation with 3,10,23,21,factor  5 had a correlation with 1,7,12 ,18

According to Cooper (2010) a minus sign indicates a negative correlation. We were able to establish item 13 belonging to factor 1 the consciousness group had a negative value of   (-507) which would indicate a question that was reverse scored. By conducting the analysis we were able to identify the responses that the participants had given to each item our specifically designed 25 questionnaire personality test.

Other Items which indicated a negative value were  6 (-.520) in the factor  3 group : Extroversion and 15  in the factor 2 group : Neuroticism (-.407) which also indicates reverse scoring questions,we were able to establish factor  2:  Neuroticism  had the highest level of responses from participants. We also established that  factor 1: consciousness  had each item scored >.5.

The item  16 (.507) loaded onto factor 2 instead of the expected factor 5,  (please see in the index)

And item 9 was omitted because it was  loaded onto factor  6, which did not feature on the PA test.

Using the following methods Kaiser-Meyer-Olkin and The Bartlett’s Test of Sphericity

The results from the Kaiser-Meyer-Olkin test demonstrated a value of 0.703  according to Field (2013) the minimum level is 0.6>x

The Bartlett’s Test of Sphericity  result  was  (df 300)= ( 2152.769,  p< 0.005)

(statistics table  in Appendix)

 

 

 

 

 

 

 

Word count 1498 total

Results 871

 

References:

Arthurs N et al (2014) Achievement for Students Who are Persistently Absent: Missing School, Missing Out? Urban Review. Dec2014, Vol. 46 Issue 5, p860-876. 17p.(Abstract only)

Cooper, C. (2010). Individual differences and personality (3rd ed.). London: Hodder Education. Retrieved from http://cw.tandf.co.uk/psychology/individual-differences-and-personality/

Statistics Canada, Education in Canada: A Statistical Review, Ottawa, 1973-2000.

Costa, P. T., & McCrae, R. R. (1992). NEO-PI(R) professional manual. Odessa, FL: Psychological Assessment Resources.

Fabrigar, L. R., & Wegener, D. T. (2012). Exploratory factor analysis. [electronic book]. Oxford; Oxford University PressChapter 17: “Exploratory factor analysis”

Field, A. (2013). Discovering Statistics using IBM SPSS statistics (4th Eds). UK: Sage Publication.

Gurven, M., von Rueden, C., Massenkoff, M., Kaplan, H., & Vie, M. L. (2013). How Universal Is the Big Five? Testing the Five-Factor Model of Personality Variation Among Forager–Farmers in the Bolivian Amazon. Journal of Personality and Social Psychology104(2), 354–370. http://doi.org/10.1037/a0030841

Horn, J. L. (1965), “A Rationale and Test For the Number of Factors in Factor Analysis,” Psychometrika, 30, 179-85.

Jolliffe, I. (1986). Principal Component Analysis. Springer Verlag.

Parallel Analysis. Retrieved from https://analytics.gonzaga.edu/parallelengine/

Stevens, J. P. (2002). Applied multivariate statistics for the social sciences (4th ed.). Hillsdale, NS: Erlbaum.

 

 

 

 

 

 

 

 

 

 

 

Appendix:

 

6 scores greater than 1

 

Total Variance Explained
Component Initial Eigenvalues Extraction Sums of Squared Loadings
Total % of Variance Cumulative % Total % of Variance Cumulative %
1 2.160 8.641 8.641 2.160 8.641 8.641
2 2.114 8.456 17.098 2.114 8.456 17.098
3 1.893 7.571 24.668 1.893 7.571 24.668
4 1.703 6.810 31.478 1.703 6.810 31.478
5 1.642 6.569 38.047 1.642 6.569 38.047
6 1.064 4.258 42.305 1.064 4.258 42.305
7 .932 3.730 46.035      
8 .907 3.626 49.661      
9 .881 3.525 53.186      
10 .866 3.462 56.648      
11 .850 3.399 60.047      
12 .828 3.312 63.359      
13 .817 3.268 66.628      
14 .805 3.221 69.848      
15 .769 3.074 72.923      
16 .756 3.025 75.948      
17 .740 2.960 78.908      
18 .727 2.907 81.814      
19 .706 2.825 84.639      
20 .684 2.734 87.373      
21 .678 2.714 90.087      
22 .668 2.673 92.760      
23 .633 2.533 95.292      
24 .596 2.383 97.676      
25 .581 2.324 100.000      
Extraction Method: Principal Component Analysis.

 

 

The factors that are above the curve ( inflection point of retaining factors

 

 

 

 

 

 

 

 

According to Horn (1965) we retain the factors that are higher from the research data, than the corresponding data which is run randomly

Component or Factor Mean Eigenvalue Percentile Eigenvalue
1 1.297120 1.335867
2 1.252433 1.283924
3 1.217893 1.246695
4 1.189013 1.212341
5 1.162260 1.184262
6 1.138026 1.159807
7 1.115636 1.137627
8 1.093496 1.114383
9 1.071495 1.088771
10 1.051154 1.068740
11 1.030922 1.048493
12 1.011218 1.027736
13 0.991996 1.008935
14 0.973965 0.989698
15 0.955395 0.970783
16 0.936674 0.953473
17 0.917567 0.934328
18 0.898220 0.915141
19 0.879027 0.896027
20 0.859719 0.877748
21 0.838560 0.856029
22 0.817029 0.835840
23 0.795043 0.814159
24 0.769624 0.792291
25 0.736516 0.765227

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

KMO and Bartlett’s Test
Kaiser-Meyer-Olkin Measure of Sampling Adequacy. .703
Bartlett’s Test of Sphericity Approx. Chi-Square 2152.769
df 300
Sig. .000

 

 

 

Factor

Items

Extraversion

4, 6, 14, 20, 25

Neuroticism

5, 8, 11, 15, 24

Openness

3, 9, 10, 21, 23

Agreeableness

1, 7, 12, 16, 18

Conscientiousness

2, 13, 17, 19, 22

 

 

 

 

 

 

Pattern Matrixa
  Factor
1 2 3 4 5
19 .543        
2 .524        
22 .519        
13 -.507        
17 .506        
8   .520      
16   .507      
11   .492      
24   .476      
5   .430      
15   -.407      
25     .524    
6     -.520    
14     .476    
20     .404    
4     .385    
9          
10       .552  
3       .535  
23       .508  
21       .423  
18         .535
1         .448
7         .448
12         .408
Extraction Method: Principal Axis Factoring.

Rotation Method: Oblimin with Kaiser Normalization.

a. Rotation converged in 4 iterations.

 

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