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 Psychology, 104(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. | |||||