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Volume 20, Number 3 1995

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A Principal Components Analysis of Factors Critical to Participation in Veterinary Lifelong Education Programs

D. J. O'Brien, J. W. Lloyd and J. B. Kaneene
From the Population Medicine Center and Department of Large Animal Clinical Sciences
College of Veterinary Medicine (O'Brien, Lloyd and Kaneene) and Department of Agricultural Economics (Lloyd)
Michigan State University, East Lansing, MI 48824-1314.


Introduction

Veterinary medicine is a dynamic profession. In order to be of maximum benefit to the patients and society it serves, the profession must respond to changes in knowledge generated by advances in medicine and all of its related specialties. The profession must also adapt to the constantly rising expectations of the public for state of the art techniques, current management information, and accountability for animal welfare and protection of the food supply. While traditional veterinary medical education may not necessarily provide the information to address all of these expectations, it is at least in a position to access the student prior to graduation from veterinary school. Subsequently, however, it may become more difficult to reach the graduate to provide updated information. Constraints on time, location of employment, and perceived lack of relevance can limit the practitioner's exposure to current information. To make continuing education valuable and justifiable to practitioners, yet cost- and time-efficient for educators, programs should be planned to facilitate attendance by the individuals at whom the programs are targeted. Consequently, information on factors critical to gain participation becomes pivotal for efficient planning of lifelong education programs.

In an earlier report (1), veterinary lifelong education interests in Michigan were investigated. In that work, some administrative factors that might influence attendance at lifelong education programs were reported. However, no attempt was made to quantitatively describe the association between past participation in lifelong education programs and these administrative factors. Quantitative description of these factors and of the relative influence each has on participation by practitioners could prove useful in planning for these education programs. Prior information suggests that some of these administrative factors may be closely correlated, a situation which, when applied to the variables in a data set which describe these factors, is known as multicollinearity. The existence of multicollinearity can interfere with the ranking of variables according to their relative contribution to a given outcome. So, to accurately rank administrative factors by their influence, one needs to employ modeling approaches that can both detect and adjust for multicollinearity before final ranking is completed.

The objectives of the present study, then, were to 1) quantitatively describe and rank some administrative factors critical to participation in veterinary lifelong education programs using a modeling approach that detects and adjusts for multicollinearity and 2) describe the association between past participation in lifelong education programs and these administrative factors.

Materials and Methods

Study Design. An assessment of the lifelong education needs of Michigan veterinarians was initiated in the autumn of 1990. The background, detailed methods and descriptive results of the instrument of this assessment, the Veterinary Lifelong Education Interests Survey, have been reported previously (1). Briefly, the survey was designed to document recent educational activities by respondents, and to describe topics of interest and administrative preferences which could be useful in planning programs to maximize participation. The survey consisted of a questionnaire mailed in January of 1991 to all 1630 known, nonretired veterinarians in Michigan. It was followed approximately two weeks later by a postcard which thanked each subject for returning the questionnaire or reminded them to do so.

Statistical Modeling. After examining the summarized descriptive statistics from the survey, a regression model was constructed to describe an association between the administrative factors expressed by respondents as being critical to their participation in veterinary lifelong education programs and the actual number of programs that each respondent reported having attended. The outcome variable in this regression (Totmt) was the sum of the total number of meetings of each of four different categories that the subject reported having attended in the past 24 months. The four categories were: 1) national meetings, which included such programs as the American Veterinary Medical Association conference, and the Eastern and Western States Veterinary conferences; 2) specialty group meetings, which included board specialties meetings such as the American College of Veterinary Internal Medicine and the American Board of Veterinary Practitioners meetings; 3) seminars, which included seminars, lecture series, and conferences sponsored by a college or school of veterinary medicine; and 4) miscellaneous meetings, which included local and regional association meetings such as local Veterinary Medical Association and regional American Animal Hospital Association meetings.

As explanatory variables in the initial regression model, the responses to the question "How critical are the following to gain your participation in continuing education programs?" were used. The administrative factors and the coding of responses are presented in Table 1. These responses were converted to binary form, with "not at all important" being given the value 0, "not important" and the other two responses being given the value 1, "Important." This coding transformation was made in order to facilitate Principal Components Analysis (2, 3).

Using SAS for personal computers (4), this regression was fitted using ordinary least squares, to obtain parameter estimates according to the equation:

Totmt=a+b1(CR1) +b2 (CR2) + . . . +b8 (CR8) + e {1}

where a is the intercept term, bi is the regression coefficient for each administrative factor, e is the residual (error) term, and the other variables are as described in Table 1.

Table 1. Coding of Responses for Administrative Factors.

How critical are the following to gain your participation in continuing education programs?
(Please circle the appropriate number for each item listed.)
 
  Not at all
Important
Somewhat
Important
Very
Important
Travel distance (CR1) 1 2 3
Program environment/setting(CR2) 1 2 3
Available program credit (CR3) 1 2 3
Days of the week on which the program is held (CR4) 1 2 3
Length of program (CR5) 1 2 3
Program format (CR6) 1 2 3
Month of the year (CR7) 1 2 3
Registration fee (CR8) 1 2 3

It was suspected from initial examination of the descriptive results of the survey that the critical administrative factors we questioned the respondents about were correlated with each other. When independent variables are correlated, multicollinearity is said to exist. If, in fact, these factors were correlated, multicollinearity might exist between our explanatory variables and so adversely affect the efficacy of our analysis, making it difficult to accurately rank the importance of the administrative factors to program attendance. For example, it was suspected that travel distance might be correlated with month of the year. In other words, if the month of the year that a program was held in was considered important, travel distance to and from the program might also be considered important (that is, a respondent might be less likely to travel long distances to a program during months when the weather is poor or unpredictable).

Both formal and informal methods exist to check for the presence of multicollinearity in a data set. One of the formal methods involves the calculation of Variance Inflation Factors (VIFs). The statistical theory behind, and the computation of, these factors has been discussed elsewhere (5). From an interpretive standpoint, the magnitude of the VIFs indicate the presence and extent of multicollinearity. A VIF equal to one indicates no linear relationship to the other explanatory variables. Mean VIFs in excess of one are indicative of the presence of multicollinearity, while VIFs greater than ten indicate serious multicollinearity problems. After evaluating the VIFs, a Principal Components Analysis (PCA), a statistical technique originated by Hotelling 6, was undertaken. While the technique has diverse and complex applications (2), in its simplest sense it is a technique that allows the transformation of a set of correlated explanatory variables into an equal number of uncorrelated variables. These new variables, know as Principal Components (PCs) are all linear combinations of the original correlated variables. The PCs can be utilized as explanatory variables in regression models to obtain parameter estimates, which can then be used to reconstitute regression coefficients for the original explanatory variables that are corrected in such a way as to minimize the effect of multicollinearity 7.

Another application of PCA is in reducing the dimensionality of a linear model by minimizing the variability that is due to correlations among the explanatory variables. It is common for some number of principal components to account for the greater part of the variability in the dependent variable, while the remaining PCs account for very little. This situation conveniently allows the exclusion of these equal or nearly equal PCs from the analysis, providing the ability to adequately represent a multivariate situation in a reduced dimensionality (2), while maintaining the significance and explanatory capabilities of the model. There are many so called "stopping rules" that can be applied to a set of PCs to evaluate them for exclusion. A commonly used stopping rule known as Bartlett's test (8) was applied to the set of PCs in this study. From this, it was determined that two of the eight PCs were not significantly different from each other and that their exclusion was thus unlikely to reduce the predictive power of the model; these were excluded from the analysis. The six retained PCs were fitted back into a regression model with the outcome variable Totmt, and parameter estimates were generated by the equation:

Totmt=a+b1(PC1) +b2 (PC2) + . . . +b6 (PC6) + e       {2}
where PCj are the principal components derived from the explanatory variables in {1}.

These parameter estimates were then used to reconstitute regression coefficients for the 8 critical administrative factors. These were ranked by magnitude and compared to the magnitude-ranked coefficients obtained from the initial regression model. These in turn were compared to rankings of the administrative factors based on the percentage of respondents who reported each administrative factor to be important 1.

Some recent uses of PCA in the fields of veterinary epidemiology and animal health economics include a study by Bigras-Poulin (9) which used the technique to reduce the number of independent variables by constructing some general factors to study farmer's attitudes and management in southern Ontario dairy herds. Lafi and Kaneene (7) have recently explained the use of the technique to detect and correct multicollinearity, and Lafi (10) utilized PCA to investigate risk factors for Repeat Breeder Cow Syndrome in Michigan dairy cattle.

Results

Of the 1630 questionnaires sent, 783 were returned, for a response of 48%. As mentioned previously, descriptive results of the survey are presented elsewhere (1). The mean total number of meetings attended in the last 24 months by respondents was 9.12 (S.D. = 8.84), with a range of 0 to 106.

The regression coefficients resulting from the fitting of the regular regression model can be found in Table 2; associated F and p-values and the r2 statistic for this model are shown in Table 3.

Table 2. Regression Coefficients for Regular and PCA Reconstituted Models and Variance Inflation Factors (VIFs).

Variable Regression
Coefficient
PCA
Reconstituted
Regression
Coefficient
VIF
Intercept 8.56 8.50  
Travel Distance -0.70 -0.58 1.12
Program Setting 1.15* 1.16 1.10
Available Credit -1.50** -1.50 1.05
Days of Week -0.72 -0.49 1.23
Length of Program 0.79 0.41 1.28
Program Format 1.76* 1.92 1.21
Month of Year 0.32 0.28 1.13
Registration Fee -1.00 -1.02 1.10
*      Significant at p _ 0.05
**    Significant at p _ 0.1

The calculated Variance Inflation Factors for the 8 explanatory variables ranged from 1.05 to 1.28, with a mean of 1.15, indicating that some multicollinearity was present as suspected, but that it was not severe. As mentioned previously, a PCA was undertaken to correct for the effect of this multicollinearity. It generated eight PCs, and after applying Barlett's Test to these, it was determined that the last two PCs were not significantly different, and they were excluded from subsequent analyses. The six retained PCs were regressed on the number of total meetings, and the parameter estimates obtained yielded the reconstituted regression model. Table 2 summarizes the coefficients for the initial regression model and the PCA regression model, and the Variance Inflation Factors for each of the administrative factors. The r2, F and p-values for the PC regression model can be found in Table 3.

The rankings of the relative importance of the administrative factors obtained from the two regression models and from the survey's descriptive statistics are presented in Table 4.

Table 3. F and p-values, and r2 statistics for Regular and PCA Regression Models.

Model F-value p-value r2
Regular Regression 1.78 0.08 0.018
PCA Regression 2.35 0.03 0.018

Table 4. Ranking of Administrative Factors Critical to Participation in Veterinary Lifelong Education Programs.

                 Ranking               
  By Value of Coefficients
Administrative
Factor
By %
Reporting Factor
as Critical
Regular
Regression
PCA
Regression
Travel Distance 1 7 5
Length of Program 2 5 7
Days of Week 3 6 6
Month of Year 4 8 8
Program Format 5 1 1
Registration Fee 6 4 4
Program Setting 7 3 3
Available Credit 8 2 2

Of the eight administrative factors used as explanatory variables in the initial regression model, two were found to be significant at p _ 0.01 (program setting and program format), and one to be significant at p _ 0.05 (available program credit).

Discussion

Several interesting points arose from these analyses. First there was a marked difference in some cases, based on these rankings, between the factors that respondents mentioned as being critical to their participation in continuing education, and the factors that statistically had the greatest effect on the total number of meetings these veterinarians attended. For instance, travel distance was mentioned in our descriptive statistics by the largest percentage of respondents (90%) as being critical to their participation, but in the regular regression model, it ended up ranked seventh out of the eight factors. In the PCA regression model, it was ranked fifth. Similarly, available program credit was mentioned by the smallest percentage of respondents (39%) as being important to their participation, yet it ended up being ranked second in importance in the regression models. It appears that what people said was important to their participation was not necessarily what had the greatest effect on their attendance in these models.

Second, using PCA to minimize the effect of multicollinearity among the predictor variables rearranged the ranking of importance of the critical administrative factors. Length of program and travel distance exchanged rankings after PCA regression, with travel distance moving up from seventh to fifth in rank, and length of program falling from fifth to seventh. It is important to note that the presence of multicollinearity, while not severe, was enough to change the rankings of importance of the administrative factors. Had PCA of these data not been undertaken (under the assumption that the extent of multicollinearity was so small that it was unlikely to affect the results), different final rankings would have resulted. As can be seen in Table 3, PCA improved the significance of the model substantially, while leaving its predictive power virtually unaffected.

Third, two points should be noted about the coefficients of the administrative factors in the regression models. The reduction of multicollinearity by PCA regression did not change the signs of any of the coefficients of the administrative factors. Signs on coefficients which are opposite those expected are considered an informal indication of multicollinearity (5, 9). The fact that none of the regression coefficients changed signs as a result of PCA may be due to the fact that the extent of multicollinearity among these predictors was not severe. Also, in interpreting these results, it is important to consider not only the relative rankings of the coefficients, but also their signs. For example, available program credit was ranked second in importance by the regression models and it carried a negative sign. This indicates that those veterinarians who considered available program credit to be important attended fewer meetings. Continuing education credit is not required for licensure in Michigan, and this may well explain the low percentage of respondents who said it was important in the descriptive statistics. But, for those who do consider it important, these results suggest that the programs in the past 2 years have apparently not done an adequate job in offering the amount or type of program credit that would gain these veterinarians' participation.

Finally, despite the fact that the regression models explained only a small proportion of the variation in the total number of meetings attended by respondents, the fact that the models were statistically significant indicates that these administrative factors were in fact important in describing actual participation in lifelong education programs. The purpose of this project was not to predict why veterinarians attend programs, but to describe the relationship between administrative factors useful to program planners and actual participation behavior.

It is also important to recognize the limitations of the present study. The population under study was confined to Michigan veterinarians, and caution should be exercised when generalizing these results to veterinarians elsewhere. The somewhat low response of 48% leaves some questions regarding the attitudes of the nonrespondents unanswered. It is possible that those who did respond may be involved with somewhat more progressive or prosperous practices where there is more interest in and more emphasis placed on continuing education. Unfortunately, there was no convenient way within the context of this study to assess whether the attitudes expressed by the respondents are representative of those who did not respond. Consequently, it is not possible to predict whether continuing education programs planned according to these results would in fact entice the nonrespondents to participate, or whether some other factor(s) not reported or not studied may be the key to gaining these veterinarians' participation. It would also be interesting to know whether the rather high number of nonresponses could be attributed to lack of interest on the part of the subjects, or whether the method of administering the questionnaire (mailing followed by a single reminder card) was simply not effective in this case. Futures studies might utilize other methods of administration (for example, mailing the questionnaire more than once or attempting telephone interviews with subjects not responding by mail) in order to increase the number of responses, and so the internal validity, of the study.

Future investigations might also consider exploring whether or not such characteristics as age, gender, year of graduation, geographic region and topics of interest affect the ranking of administrative factors critical to participation. Statistical modeling techniques could be readily adapted to address these and other questions. As this study has pointed out, while descriptive statistics are certainly helpful, they do not necessarily provide all of the information that is useful and needed to efficiently plan continuing education programs that will gain maximum participation.

Summary

In summary, the results of the Michigan Veterinary Lifelong Education Interests Survey were utilized as a database from which to establish, by statistical modeling, the relative ranking of administrative factors critical to participation in veterinary lifelong education programs. The models were also used to describe the association between these administrative factors and respondents' past participation in such programs. A Principal Components Analysis was undertaken to describe and correct for the effect of multicollinearity among these administrative factors in the statistical models. Substantial disparities were found to exist between rankings of the administrative factors based on the percentage of respondents that reported the factor as being critical to participation, and those based on the effect the factor had on the total number of meetings attended in the statistical models. Correction for multicollinearity by PCA was found to affect the ranking of the factors as well. It was concluded that in order to efficiently plan lifelong education programs to maximize participation, consideration should be given not only to the expressed preferences of respondents, but to statistical techniques that describe the relationship between these preferences and actual past attendance.

References and Endnotes

1. Lloyd JW, Lloyd LD, Hickey H, Kaneene JB, Sawyer DC: Veterinary lifelong education interests in Michigan. Jour Vet Med Educ 19(4): 118-122, 1992.

2. Jackson JE: A User's Guide to Principal Components. New York: John Wiley & Sons, Inc., 1991, 569 pp.

3. Gower JC: Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53:325-338, 1966.

4. SAS Institute, Inc. SAS/STAT User's Guide, Version 5 Edition, SAS Institute, Inc., Cary, N.C., 1986.

5. Neter J and Wasserman W: Applied Linear Statistical Models: Regression, Analysis of Variance, and Experimental Designs, ed 5. Homewood, IL: Richard D. Irwin, Inc., 1985, pp 391-392.

6. Hotelling H: Analysis of a complex of statistical variables into principal components. J Educ Psychol 24:417-441, 498-520, 1933.

7. Lafi S and Kaneene JB: An explanation of the use of principal components analysis to detect and correct multicollinearity. Prev Vet Med 13:261-275, 1992.

8. Anderson TW: Asymptotic theory for principal component analysis. Ann Math Stat 34:122-148, 1963.

9. Bigras-Poulin M: PhD thesis, University of Guelph, Guelph, Ontario, 1985.

10. Lafi S: Epidemiologic and economic study of Repeat Breeder Syndrome in Michigan dairy cattle. PhD thesis, Michigan State University, East Lansing, MI, 1989.


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