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Factor Analysis, Research Paper Example

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Words: 2773

Research Paper

Abstract:

This paper looked at the topic of factorial analysis in two settings: 1) An statistical analysis of an existing data sex (Auto Loan.Xls) to understand potential factors in the sales of new cars.  The statistical analysis found that three factors were useful in understanding predictors for a new car: 1) factors related to price; 2) factors related to fuel and engine characteristics; 3) wheelbase and miles per gallon (negatively correlated).

In addition three academic papers were examined for their treatment of factor analysis in different fields: 1) business; 2) nursing; 3) public health.  Overall, it was shown that factor analysis can play a key role in understanding and separating correlating factors among different variables.

Introduction

This paper will examine the concept of factor analysis in statistical analysis.  Factor analysis is typically used when researchers are trying to understand what (and how many) potential variables compose a data set.  The strengths of factor analysis allows the researcher to tease out if variables have similar correlations while dealing with the problem of multicollinearity Indeed, while factor analysis was originally (and primarily) used in the field of psychology, it has expanded to other fields of study.

This paper will try to accomplish two things.  First, the paper will analyze a data set of characteristics related to car sales.  By using a correlation matrix and applied factor analysis, predictive factors of the data set will be established.  Second, academic papers will be examined to understand how factor analysis is used in different contexts.  In particular, this paper will look at papers that look at stock returns, why nurses don’t research more, and public health issues.

 

Data Analysis:

 

The data analysis for this paper will focus on the data set (CarSales,xls), a data set that has 26 variables and 158 observations (note: some observations are missing).  In order to conduct a proper factor analysis, the first step is to analyze the existing data set (“CarSales.Xls) to find out the correlations among existing variables.  Although the initial data set consisted of 26 variables, 3 variables (manufacturer, model, type) were expunged from the data set because they were not continuous variables and not deemed highly relevant to the analysis.

The results of the correlation coefficient analysis are included in the appendix of this report.  Upon inspection, many of the variables are highly correlated (either in a positive or negative manner), and although many might have high correlations, such as log and other variables, they will be left in to see what the factor analysis provides.

The results of the actual factor analysis are included in the appendix. Judging from the scree plot and the correlation matrix, there are 3 different factors included in this analysis.  The first factor includes variables that are related to price; the second factor is variables related to fuel and engine characteristics.  The third factor is variables related to wheelbase and miles per gallon.  Overall, looking at the summary statistics associated with the analysis, this results looks to be robust.

III. Academic Paper Review

 

The three academic papers examined in this paper all implement factor analysis to examine data used in different fields of analysis. Hicks (1996) leverages factor analysis a key analytical method in exploring why nurses have lower research output than other trained clinicians (such as doctors).  Indeed, while 71% of respondent nurses reported that they had conducted research of some kind, only 5% had published results in a professional journal (Hicks, 1996).  The first step in understanding why nurses do not publish more research was to develop a valid psychological scale: Hicks developed the questions from the existing literature and pre-and post-interviews with nurses in the field.   After the research was completed, a total of 38 attitude statements (that were ultimately reduced to 13 item scales) were created on a 5-point Likert scale that would allow the individual to express the level of agreement (disagreement) with a series of statements given to 500 qualified nurses.     

 

After the surveys were taken, there were a total of four  factors identified with face validity.  The first factor, accounting for 18.5% of responses, were subjective/ personal barriers to research related to lack of motivation, interest, confidence, and belief in the value of nursing research.  This factor was also found to be a statistically significant barrier (via a t-test) versus nurses who conducted research.  The second factor, which accounted for 11.9% of the total variance, was identified as organizational or structural barriers to research. The third factor, accounting for 10.6% variance in the data set, is the respondents’ concern regarding medical opinion of nursing research.  The fourth factor identified was that nurses lack the confidence in  their own research and the findings being used in medical practice.  The fifth factor was ‘impact of nursing research’ that the lack of research had on the clinical practice.  Overall, these factors were found to be robust in face validity tests explaining why

 

Hendrie et al. (2010) use factor analysis as a means to identify predictors between a family activity environment.  Obesity is a major topic of concern in both medical and political circles.  Of potential interest is how children become obese: that is, are the factors primarily genetic in nature, or does family environment also play a key role in the “obesity” epidemic.  To explore this issue, Hendrie et al. The researchers recruited children volunteers, of which consisted of 106 parents of children aged 5-11 years.  The parents were asked to measure the children’s activity levels using the CLASS survey that includes questions of  the amount of television watched, electronic gaming, and participation in exercise (both moderate and vigorous).  At the same time, the survey also measured the child’s diet on a daily basis.  The questionnaire included 29 items about the family activity environment.

 

After analyzing the surveys, three main factors were identified that accounted for 37.6% of the total variance.  The first factor, “parental involvement”, had a total of 14 items and described the parent’s involvement in their kid’s education. The second factor was described as “opportunities for role modeling” that primarily included variables related to interaction between parents and children in the realm of either activity or non-activity.  The third factor is “parental support” and dealt with direct support for a child’s activity. Overall, the study found, by looking at the different factors, socioeconomic status and parental involvement played a key role in the process.

 

Finally, Gibbons (1986) used factor analysis to see what potential factors make up the arbitrage pricing theory.  In particular, Gibbons works on identifying factors that are key predictors of stock price.  The author looked at 41 different portfolios of NYSE stocks with monthly data from 1951-1971.  The paper states that the final model includes both market and industry factors for analysis.  The market factor includes the basic statistical description of the market, while the industry factor depends on the different industry that the firm is in.

 

 

References:

Gibbons, M.R. (1986).  Empirical Examination of the Return Generating Process of the Arbitrage Pricing Theory.  Stanford Graduate School of Business Paper. Available at: https://gsbapps.stanford.edu/researchpapers/library/RP881.pdhttps://gsbapps.stanford.edu/researchpapers/library/RP881.pd.  

Hicks, C. (1996). A study of nurses’ attitudes towards research: a factor analytic approach. Journal of Advanced Nursing. 23 , 373-379.

Hendrie, G.A., Conveney, J., & Cox, D.N. Factor analysis  shows association between family activity environment and child’s health environment. Australian and New Zealand Journal of Public Health, 35(6), 524-529 

 

Appendix 1:

 

Descriptive Statistics
Mean Std. Deviation Analysis N
resale 18.03 11.606 117
price 25.97 14.150 117
engine 3.05 1.055 117
horsepower 181.28 58.592 117
wheelbase 107.33 8.051 117
width 71.19 3.530 117
length 187.72 13.850 117
curb_wgt 3.32 .597 117
fuel_cap 17.81 3.795 117
mpg 24.12 4.404 117
lnsales 3.40 1.338 117
zresale .00 1.013 117
ztype -.03 .984 117
zprice -.10 .986 117
zengine -.01 1.010 117
zhorsepower -.08 1.033 117
zwheelbase -.02 1.054 117
zwidth .01 1.023 117
zlength .03 1.031 117
zcurb_wg -.09 .947 117
zfeul_ca -.04 .976 117
zmpg .06 1.028 117

 

 

Correlation Coefficient
sales resale price engine horsepower wheelbase width length curb_wgt fuel_cap mpg lnsales zresale
sales Pearson Correlation 1 -.279** -.305** .020 -.198* .358** .141 .255** .009 .087 -.017 .731** -.279**
Sig. (2-tailed) .002 .000 .804 .013 .000 .079 .001 .915 .283 .837 .000 .002
N 157 121 155 156 156 156 156 156 155 156 154 157 121
resale Pearson Correlation -.279** 1 .954** .531** .769** -.052 .179 .027 .362** .326** -.400** -.525** 1.000**
Sig. (2-tailed) .002 .000 .000 .000 .571 .051 .773 .000 .000 .000 .000 .000
N 121 121 119 120 120 120 120 120 119 120 119 121 121
price Pearson Correlation -.305** .954** 1 .627** .840** .111 .329** .157 .526** .423** -.492** -.553** .954**
Sig. (2-tailed) .000 .000 .000 .000 .171 .000 .051 .000 .000 .000 .000 .000
N 155 119 155 155 155 155 155 155 154 155 153 155 119
engine Pearson Correlation .020 .531** .627** 1 .837** .472** .690** .541** .760** .663** -.735** -.139 .531**
Sig. (2-tailed) .804 .000 .000 .000 .000 .000 .000 .000 .000 .000 .084 .000
N 156 120 155 156 156 156 156 156 155 156 154 156 120
horsepower Pearson Correlation -.198* .769** .840** .837** 1 .286** .539** .393** .610** .500** -.611** -.387** .769**
Sig. (2-tailed) .013 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
N 156 120 155 156 156 156 156 156 155 156 154 156 120
wheelbase Pearson Correlation .358** -.052 .111 .472** .286** 1 .683** .840** .651** .654** -.498** .293** -.052
Sig. (2-tailed) .000 .571 .171 .000 .000 .000 .000 .000 .000 .000 .000 .571
N 156 120 155 156 156 156 156 156 155 156 154 156 120
width Pearson Correlation .141 .179 .329** .690** .539** .683** 1 .710** .721** .656** -.603** .041 .179
Sig. (2-tailed) .079 .051 .000 .000 .000 .000 .000 .000 .000 .000 .609 .051
N 156 120 155 156 156 156 156 156 155 156 154 156 120
length Pearson Correlation .255** .027 .157 .541** .393** .840** .710** 1 .627** .564** -.447** .217** .027
Sig. (2-tailed) .001 .773 .051 .000 .000 .000 .000 .000 .000 .000 .007 .773
N 156 120 155 156 156 156 156 156 155 156 154 156 120
curb_wgt Pearson Correlation .009 .362** .526** .760** .610** .651** .721** .627** 1 .864** -.818** -.040 .362**
Sig. (2-tailed) .915 .000 .000 .000 .000 .000 .000 .000 .000 .000 .621 .000
N 155 119 154 155 155 155 155 155 155 155 153 155 119
fuel_cap Pearson Correlation .087 .326** .423** .663** .500** .654** .656** .564** .864** 1 -.802** -.017 .326**
Sig. (2-tailed) .283 .000 .000 .000 .000 .000 .000 .000 .000 .000 .836 .000
N 156 120 155 156 156 156 156 156 155 156 154 156 120
mpg Pearson Correlation -.017 -.400** -.492** -.735** -.611** -.498** -.603** -.447** -.818** -.802** 1 .120 -.400**
Sig. (2-tailed) .837 .000 .000 .000 .000 .000 .000 .000 .000 .000 .139 .000
N 154 119 153 154 154 154 154 154 153 154 154 154 119
lnsales Pearson Correlation .731** -.525** -.553** -.139 -.387** .293** .041 .217** -.040 -.017 .120 1 -.525**
Sig. (2-tailed) .000 .000 .000 .084 .000 .000 .609 .007 .621 .836 .139 .000
N 157 121 155 156 156 156 156 156 155 156 154 157 121
zresale Pearson Correlation -.279** 1.000** .954** .531** .769** -.052 .179 .027 .362** .326** -.400** -.525** 1
Sig. (2-tailed) .002 .000 .000 .000 .000 .571 .051 .773 .000 .000 .000 .000
N 121 121 119 120 120 120 120 120 119 120 119 121 121
ztype Pearson Correlation .242** -.089 -.044 .259** .005 .388** .246** .135 .523** .597** -.575** .274** -.089
Sig. (2-tailed) .002 .330 .585 .001 .954 .000 .002 .092 .000 .000 .000 .001 .330
N 157 121 155 156 156 156 156 156 155 156 154 157 121
zprice Pearson Correlation -.305** .954** 1.000** .627** .840** .111 .329** .157 .526** .423** -.492** -.553** .954**
Sig. (2-tailed) .000 .000 .000 .000 .000 .171 .000 .051 .000 .000 .000 .000 .000
N 155 119 155 155 155 155 155 155 154 155 153 155 119
zengine Pearson Correlation .020 .531** .627** 1.000** .837** .472** .690** .541** .760** .663** -.735** -.139 .531**
Sig. (2-tailed) .804 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .084 .000
N 156 120 155 156 156 156 156 156 155 156 154 156 120
zhorsepower Pearson Correlation -.198* .769** .840** .837** 1.000** .286** .539** .393** .610** .500** -.611** -.387** .769**
Sig. (2-tailed) .013 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
N 156 120 155 156 156 156 156 156 155 156 154 156 120
zwheelbase Pearson Correlation .358** -.052 .111 .472** .286** 1.000** .683** .840** .651** .654** -.498** .293** -.052
Sig. (2-tailed) .000 .571 .171 .000 .000 .000 .000 .000 .000 .000 .000 .000 .571
N 156 120 155 156 156 156 156 156 155 156 154 156 120
zwidth Pearson Correlation .141 .179 .329** .690** .539** .683** 1.000** .710** .721** .656** -.603** .041 .179
Sig. (2-tailed) .079 .051 .000 .000 .000 .000 .000 .000 .000 .000 .000 .609 .051
N 156 120 155 156 156 156 156 156 155 156 154 156 120
zlength Pearson Correlation .255** .027 .157 .541** .393** .840** .710** 1.000** .627** .564** -.447** .217** .027
Sig. (2-tailed) .001 .773 .051 .000 .000 .000 .000 .000 .000 .000 .000 .007 .773
N 156 120 155 156 156 156 156 156 155 156 154 156 120
zcurb_wg Pearson Correlation .009 .362** .526** .760** .610** .651** .721** .627** 1.000** .864** -.818** -.040 .362**
Sig. (2-tailed) .915 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .621 .000
N 155 119 154 155 155 155 155 155 155 155 153 155 119
zfeul_ca Pearson Correlation .087 .326** .423** .663** .500** .654** .656** .564** .864** 1.000** -.802** -.017 .326**
Sig. (2-tailed) .283 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .836 .000
N 156 120 155 156 156 156 156 156 155 156 154 156 120
zmpg Pearson Correlation -.017 -.401** -.492** -.735** -.611** -.498** -.603** -.447** -.818** -.802** 1.000** .120 -.401**
Sig. (2-tailed) .837 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .138 .000
N 154 119 153 154 154 154 154 154 153 154 154 154 119

 

 

 

Total Variance Explained
Component Initial Eigenvalues Extraction Sums of Squared Loadings Rotation Sums of Squared Loadings
Total % of Variance Cumulative % Total % of Variance Cumulative % Total % of Variance Cumulative %
1 12.171 55.322 55.322 12.171 55.322 55.322 7.151 32.507 32.507
2 4.927 22.397 77.719 4.927 22.397 77.719 6.915 31.433 63.939
3 1.796 8.164 85.883 1.796 8.164 85.883 4.828 21.944 85.883
4 .861 3.914 89.798
5 .681 3.096 92.894
6 .479 2.178 95.072
7 .297 1.349 96.421
8 .264 1.200 97.621
9 .235 1.067 98.688
10 .136 .618 99.306
11 .109 .495 99.801
12 .044 .199 100.000
13 7.866E-6 3.576E-5 100.000
14 5.033E-12 2.288E-11 100.000
15 4.688E-12 2.131E-11 100.000
16 4.255E-12 1.934E-11 100.000
17 3.858E-12 1.754E-11 100.000
18 3.067E-12 1.394E-11 100.000
19 2.879E-12 1.309E-11 100.000
20 2.326E-12 1.057E-11 100.000
21 2.065E-12 9.386E-12 100.000
22 1.805E-12 8.205E-12 100.000
Extraction Method: Principal Component Analysis.

 

 

 

 

Rotated Component Matrixa
Component
1 2 3
price .949 .101 .151
zprice .949 .101 .151
resale .938 -.060 .127
zresale .938 -.060 .127
zhorsepower .874 .364 .150
horsepower .874 .364 .150
zengine .643 .526 .344
engine .643 .526 .344
lnsales -.615 .286 .063
length .057 .953 .120
zlength .057 .953 .120
zwheelbase -.130 .850 .345
wheelbase -.130 .850 .345
zwidth .218 .806 .302
width .218 .806 .302
ztype -.244 .017 .886
mpg -.386 -.347 -.778
zmpg -.387 -.347 -.778
zfeul_ca .243 .474 .777
fuel_cap .243 .474 .777
curb_wgt .351 .608 .638
zcurb_wg .351 .608 .638
Extraction Method: Principal Component Analysis.

Rotation Method: Varimax with Kaiser Normalization.

a. Rotation converged in 5 iterations.

 

 

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