Evaluating the RIASEC Circumplex Using High-Point ... - ScienceDirect

JOURNAL

OF VOCATIONAL

BEHAVIOR

41, 295-311 (1992)

Evaluating the RIASEC Circumplex Using High-Point Codes TERENCE Department

of Educational

J. TRACEY AND JAMES ROUNDS

Psychology.

University

of lllinois

at Urbana--Champaign

The fit of the circumplex structure to Holland RIASEC codes was examined using loglinear analysis. Two letter high-point code frequency tables of the four Self-Directed Search norm samples (male college students, female college students, male high school students. and female high school students) and Holland’s translation of Dictionary of Occupational Titles (DOT) occupations were examined with respect to how they met the assumptions involved in Holland’s circumplex model. Results indicated that when account was taken of base rate differences in Holland codes. the circumplex model was a good fit to the data. The results have implications for the measurement of RIASEC types and the definition and interpretation of Holland’s constructs of consistency and person-environment congruence. 851IW? Academic Press. Inc.

In his theory of vocational personalities and work environments, Holland (1973. 1985a) posited that there are six personality types and six corresponding work environments: Realistic (R), Investigative (I), Artistic (A). Social (S), Enterprising (E), and Conventional (C). Rounds, Tracey, and Hubert (1992) have discussed two forms or representations of Holland’s model-the circular order hypothesis and the circumplex hypothesis-that have been evaluated in the vocational literature. The Holland’s circular order model hypothesizes that the six personality types and work environments are arranged in a circular order (R-I-A-S-E-C) with the interpoint distances among types representing the relations among the types. Because Holland depicts the RIASEC types forming an equilateral hexagon, several authors (Fouad, Cudeck, & Hansen, 1984; Hogan, 1983) have proposed that the RIASEC circular arrangement forms a circumplex structure. The circumplex structure is a more exact and specified model than the circular order hypothesis and thus of greater heuristic value. The purpose of the present study was to examine the validity of the circumplex structure for both RIASEC personality types and work environments using two letter high-point codes, instead of the more typical correlation matrix. A circumplex, according to Guttman (1954). is defined as a circular Reprint requests should be addressed to Terence J. Tracey. 210 Education, University of Illinois at Urbana-Champaign. 1310 South Sixth Street. Champaign. IL 61820. 295 0001-8791192$S.OO Copyright ‘5’ 1992 by Academic Press. Inc. All right? of reproduction in any form reserved.

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arrangement of variables where the relations among adjacent variables are equal, as are those among variables one place removed on the circle, as are those among variables two places removed on the circle, and so on. Furthermore, the relations among adjacent variables are greater than those among variables one place removed, which are greater than those two places removed, and so on. With respect to Holland’s hexagon, the circumplex would summarize the relations among the six types as all adjacent types would be equally related (RI = IA = AS = SE = EC = CR), all alternate types would be equally related (RA = IS = AE = SC = ER = CI), all opposite types would be equally related (RS = IE = AC), and the relations among adjacent types would be greater than the relations among alternate types which in turn would be greater than the relations among opposite types. Since a circumplex is more explicit and has been defined in exact testable form, we use the term RIASEC circumplex to describe Holland’s model rather than the more familiar term of hexagon. The present article evaluates the fit of the circumplex to RIASEC data rather than the fit of Holland’s circular order hypothesis. With the exception of Fouad, et al’s (1984) study on the circumplex structure in the Strong Interest Inventory General Occupational Themes and Tracey and Rounds’ (in press) examination of the fit of the circumplex structure across 104 different RIASEC matrices, researchers have been evaluating the circular order model. The circumplex model, however, is a more complete model of the RIASEC relations that has implications for methods of assessing Holland’s concepts of consistency and congruence. Research on the structure of RIASEC types (e.g., Cole & Hansen, 1971; Gati, 1991; Prediger, 1982; Rounds, in press) has typically used correlations as the means of examining relations. Correlations, however, do not capture the information most important to practice and some research. As the RIASEC scores are used in test interpretation, the focus is on the highest one, two, or three codes, called high-point RIASEC codes, that characterize a person or environment. Examination of correlations, however, ignores level differences that are crucial in the determination of high-point codes. So, results yielded from the examination of correlations may not necessarily apply to the high-point codes. High-point codes are the components used in examining the relations within personality types and work environments (i.e., consistency) as well as between personality types and work environments (i.e., congruence). As discussed by Holland (1985a), consistency of personality types and work environments are defined by an exact, equilateral hexagon or circumplex. For example, a person who has a high-point code that represents types that are in close proximity on the circumplex (e.g., adjacent types such as R and I) is viewed as being equally consistent as someone having a high-point code of different but similarly proximate types (e.g., adjacent

RIASEC

CIRCUMPLEX

297

types such as A and S), and more consistent than someone who has a high-point code that represents types that are farther apart on the circumplex (e.g., opposite types such as R and S). Similarly, work environments can vary in consistency as defined by the relative placement of the high-point codes on the circumplex. High-point codes are also instrumental in examining the congruence of person and work environments. Given high-point codes for a person and a work environment, it is possible to generate predictions about satisfaction and other vocational outcomes. The common methods for examining person-environment congruence, however, do not build upon the RIASEC structure. Neither the Zener and Schnuelle (1976) nor the Iachen (1984) indices take into account the relations depicted within a circumplex structure. Using either the Zener-Schnuelle or Iachen index, the congruence of an IR person is the same in an AS or an SE environment because they focus only on agreement without recognition of the proximity of RIASEC types. However, if the structural properties of the circumplex are correct, an IR person is more congruent in an AS environment than in an SE environment. Thus, important predictions inherent in the Holland’s model are lost by using indices that ignore the circumplex structure. If both the personality types and work environments can be validly characterized by a circumplex, then more specific predictions can be generated regarding the effects of congruence. Fundamental to Holland’s theory is a parallel person-environment RIASEC typology. Structural tests, however. have generally focused on the personality type data (vocational interests) rather than occupational data (Holland, 1985a; Holland & Gottfredson, 1990). When occupational environments have been examined, research efforts have been directed toward occupational reinforcer patterns (Borgen, Weiss, Tinsley, Dawis, & Lofquist. 1972) and job analysis data to determine if the RIASEC circular order is supported (Gottfredson, 1980; Holland. Viernstein, Kuo. Karweit, & Blum, 1972; Hyland & Muchinsky. 1991; Rounds, Shubsachs. Dawis, & Lofquist, 1978; Toenjes & Borgen, 1974). When RIASEC codes assigned to represent occupations are directly studied, the test of the circular structure is conducted by comparing the relative frequencies of consistent work environments to inconsistent work environments (Gottfredson, 1977; Gottfredson, Holland. & Gottfredson, 1975; Gottfredson & Holland, 1989). Although the results of occupational studies have been, in general, supportive of Holland’s structural formulations, missing from these studies are direct tests of how well Holland’s model fits occupational high-point codes. Given the centrality of Holland’s RIASEC codes in practice and research, the purpose of the present study was to examine the structural validity of the circumplex as it applies to high-point codes. Log-linear analysis was used to evaluate how well a circumplex structure fits distri-

298

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butions of Holland codes. In the present study, both occupational and personality type data were evaluated. The former evaluation constituted a direct structural test of Holland’s occupational classification. Given that personality types have been found to vary across age and sex (Holland, 1985a), we examined the fit of the circumplex for male and female, college and high school students. Though we examined the fit of the circumplex model to the data, we did not expect frequencies of two letter high-point codes to adhere to the circumplex because of the obvious differences in the base rates of the different types and environments. The circumplex assumes equal frequencies within adjacent, alternate, and opposite codes on the hexagon (e.g., the frequency of the adjacent high-point code SE would equal the frequency of the adjacent code RC). Given the greatly different base rates in the distribution of high-point codes, it is unlikely that the frequencies of all adjacent types would be found equal as well as all alternate or opposite types. Furthermore, Holland (1985a) claims that his hexagon accounts for the relations among the different types and environments, but no claim is made that the hexagon model would result in equal highpoint code frequencies. However, we did expect the circumplex to fit the data when the differences in the base rates of each of the types were taken into account. This modified circumplex structure, where account is taken of base rates and proportional equality of codes is assumed instead of exact equality of frequencies, was labeled a quasi-circumplex. We hypothesized that the quasi-circumplex, not the circumplex, would be an adequate representation of the data. METHOD Samples The data were obtained from published sources. The personality type data came from the Self-Directed Search (SDS) norms (Holland, 1985b, 1987). Four frequency distributions of SDS high-point codes were used: college males (Holland, 1985b. p. 73; N = 1378), college females (Holland, 1985b, p. 74; N = 1508), high school males (Holland, 1985b, p. 71; N = 2169), and high school females (Holland, 1985b, p. 72; N = 2447). The SDS is a self-administered and self-scoring measure used for vocational counseling purposes. The two highest RIASEC raw scores are designated as the high-point code. The SDS normative data are accidental samples drawn from four research reports. As described by Holland (1985b), the high school sample includes students from 12 schools in four states with most of the students being in 11th grade. The college sample includes students from 10 colleges and universities in nine states with the majority of students being in their freshmen and junior years. The work environment data came from Gottfredson and Holland’s

RIASEC

CIRCUMPLEX

299

(1989) assignment of RIASEC codes to all occupations in the Dictionary Titles (U.S. Department of Labor, 1977). The frequency distribution of high-point codes for 12,099 DOT occupations was used (Gottfredson & Holland, 1989, p. 551-552). The assignment of RIASEC codes to the 12,099 DOT occupations was accomplished with classificatory functions. Multiple discriminant analysis was used to develop classificatory functions based on occupational analysis data and occupations that had previously been assigned RIASEC codes. Support for the DOT RIASEC codes comes from a cross-classification of the 12099 DOT occupations by Holland’s categories and the Guide for Occupational Exploration (GOE; U.S. Department of Labor, 1979) interest categories. Overall, 76.80 of the DOT occupations in Holland’s RIASEC classification were correctly classified by the GOE categories (Gottfredson & Holland, 1989). The cross-classification tables for the five high-point code distributions are presented in Table 1. of Occupational

Models

To gain a thorough understanding of the data, several models were examined, though not all were thought to be theoretically related to Holland’s assumptions. The models of most importance were the circumplex and the quasi-circumplex, with the main difference between the two being the incorporation of base rate differences. Several other models were examined (specifically, symmetry, marginal homogeneity, quasi-symmetry, and quasi-independence) to provide information regarding the form of the data in the event that the circumplex or quasi-circumplex models did not hold. The major model examined was the circumplex and a depiction of the assumptions involved in a circumplex are presented in the top section of Table 2. The frequencies of all combinations of adjacent codes (e.g.. RI, IA, CR) are viewed as equal (labeled as parameter f,‘s in Table 2), all combinations of alternating codes (e.g., RA, IS, CI) are viewed as equal (parameter fi), and finally all combinations of opposite codes (RS, AC, IE) are viewed as equal (parameter f3). Further, the frequencies of adjacent codes are assumed to be greater than the frequencies of alternate codes which are in turn assumed to be greater than the frequencies of opposite codes (i.e., f, > f2 > f3). So a circumplex, a very parsimonious model, accounts for all 30 different two letter high-point code relations with only three frequency parameters. Besides, the circumplex, we examined the following four related models: symmetry, marginal homogeneity, quasi-symmetry, and quasi-circumplex. Each of these models is implied in a circumplex, but can be valid in and of itself without the circumplex being valid. Symmetry refers to the equality of high-point codes regardless of the order. e.g., the frequency of IR is equal to the frequency of RI. The

TABLE 1 Cross-Classification of High-Point Codes by Five Data Sources Second digit high-point code First digit high-point code

R

Realistic (R) Investigative (I) Artistic (A) Social (S) Enterprising (E) Conventional (C) Total Percentage

190 10 42 15 2 259 19

Realistic (R) Investigative (I) Artistic (A) Social (S) Enterprising (E) Conventional (C) Total Percentage

-

Realistic (R) Investigative (I) Artistic (A) Social (S) Enterprising (E) Conventional (C) Total Percentage Realistic (R) Investigative (I) Artistic (A) Social (S) Enterprising (E) Conventional (C) Total Percentage Realistic (R) Investigative (I) Artistic (A) Social (S) Enterprising (E) Conventional (C) Total Percentage

I

A

S

E

Self-Directed Search college males 171 23 49 18 61 167 39 26 61 10 80 50 136 23 10 86 8 0 1.5 21 308 144 378 224 22 10 27 16

Self-Directed 9 11 1 40 13 205 0 4 0 9 25 267 02 18

Search college females 1 2 0 61 142 4 199 7 417 186 5 14 35 3 3 519 360 200 34 24 13

Self-Directed Search high school males 290 111 301 128 202 61 171 46 31 38 89 20 102 96 67 138 24 16 10 68 13 9 1 21 17 372 449 250 650 349 17 21 12 30 16 -

Self-Directed Search high school 5 0 8 11 37 138 4 31 251 23 307 595 1 3 1 18 3 5 19 231 14 351 652 646 02 14 27 26

251 9 77 332 1090 1759 15

10 17 2 17 19

Total

%

271 474 109 325 153 46 1378

20 34 08 24 11 03

0 12 2 122 1 137 09

12 230 249 943 24 50 1508

01 15 16 63 02 03

39 13 0 32 15

869 493 178 435 133 61 2169

40 23 08 20 06 03

14 195 308 1632 27 271 2447

01 08 13 67 01 11

8070 364 149 551 1339 1626 12099

67 03 01 05 11 13

65 0.5

99 OS

females 1 0 2 7 9 13 274 433 4 13 299 457 12 19

Dictionary of Occupational Titles 956 13 682 4087 1 40 68 3 19 116 29 3 379 31 43 863 3 0 340 193 1022 60 1944 4843 08 00 16 40 300

C

2332 4 2 63 70 2471 20

301

RIASEC CIRCUMPLEX TABLE 2 Parameters Assumed in RIASEC Circumplex and Symmetry Models Second digit high-point code First digit high-point code

R

I

A

S

E

C

Circumplex Realistic (R) Investigative (I) Artistic (A) Social (S) Enterprising (E) Conventional (C)

fl

PI

x fi ; fI

fI Symmetry

Realistic (R) Investigative (I) Artistic (A) Social (S) Enterprising (E) Conventional (C)

fi

f2 fb

; f8 fv

fi,, :::

Note. Within each model. identical subscripts indicate that the parameters have equal values (e.g., all f,‘s are equal). For the circumplex model. the following additional constraints are also applied: f, > f2 > f3. Quasi-circumplex and quasi-symmetry models have the same frequency pattern except account is taken of marginal totals and exact equality of frequencies is not assumed, just proportional equality given marginal differences.

frequency for each high-point code is thus viewed as equal to the frequency of the transpose of the same high-point code. The frequency parameters for a symmetry model are presented in the bottom section of Table 2. In this symmetry model, the 30 different cells of high-point codes are represented by 15 frequency parameters. For symmetry to be true, the nested models of marginal homogeneity and quasi-symmetry must also be true. Marginal homogeneity is the assumption that the frequencies in the marginals are equal (i.e.. the frequencies for each of the first letter codes is equal to the frequencies for each of the second letter codes). For example, the frequency of first letter codes of S is equal to the frequency of second letter codes with S. Quasi-symmetry is identical to symmetry except there is no assumption of marginal homogeneity included. The frequencies of each two-letter high-point code are equal to the frequencies of its two-letter transpose after account has been taken of marginal differences. In quasi-symmetry, the frequencies are symmetrical to the extent that the marginals permit. thus the frequencies are proportionately symmetrical. A quasi-circumplex, the model hypothesized to be the best fit to the data, is similar to a circumplex except that it does not require exact matching of frequencies across the three parameters, only proportional

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matching with base rate probabilities taken into account. No assumption of marginal homogeneity is necessary for a quasi-circumplex, whereas it is necessary for the complete circumplex. So in the quasi-circumplex model, the conditional probabilities (i.e., frequencies after account is taken of marginal differences) are set to be equal, not the frequencies themselves as is true in the complete circumplex model. In addition to examining the validity of the circumplex model and its nested models, we also examined the assumption of quasi-independence. This quasi-independence model is identical to the typical chi-squared test of independence (i.e., the distribution of high-point codes is random after account is taken of the base rates of both the first and second letter highpoint codes) except that the main diagonal is ignored. In the context of six RIASEC categories used, acceptance of quasi-independence implies quasi-symmetry, but acceptance of quasi-symmetry does not imply quasiindependence. So a total of six models were examined in each sample: circumplex, symmetry, marginal homogeneity, quasi-symmetry, quasi-circumplex, and quasi-independence. Model Fit The log-linear procedures outlined by Wickens (1989) and Clogg, Eliason, and Grego (1990) were used to test the six models. The analysis was conducted using the BMDP program 4F (Dixon, 1988). Four indices were used to assess the model-data fit: maximum likelihood goodness of fit index (G*), the normed (NFI) and nonnormed (NNFI) fit indices, and the Baysian Information Criterion (BIG). The G* index compares the actual data to the data generated by the hypothesized model and has a chi-squared distribution. The larger the G* values, the poorer the fit. Nonsignificant results indicate a good fit to the data. Statistical significance, however, is greatly affected by sample size and model complexity. With very large samples, very few models, even a true model, could be found to yield a nonsignificant G*. With small samples, many models, even a very inaccurate model, could yield a nonsignificant result and thus be accepted. Given the very large sample sizes examined in this study, this bias toward rejecting adequate models in contexts with large sample sizes is especially salient. Further, more complex models are frequently accepted over more parsimonious, though true, models, because the more complex models account for more error. Sample size and model complexity must, thus be taken into account when interpreting the G* goodness of fit index. As a way of partially correcting for these sample size and model complexity effects, Bonett and Bentler (1983) have advocated the use of two descriptive fit indexes: the normed (NFI) and nonnormed (NNFI) fit indices. These indices compare the fit of the hypothesized model to the data with the fit of a null model, where all cells of the table are equal.

.

RIASEC CIRCUMPLEX

303

The NFI represents the percentage of improvement in the goodness of fit over the null model. The NFI index ranges from zero to 1.00 and has a value of 1.00 when the model fits the data perfectly. A value of zero indicates that the tested model is no better than a null model of complete equality in frequencies across all cells. The NNFI is similar to the NFI except the number of degrees of freedom is taken into account. The greater the number of degrees of freedom, the fewer parameters that need to be explained or estimated in a model. Therefore. NNFI is also an indicator of parsimony. If two models yield similar NFI values, yet one has a larger NNFI, the one with the larger NNFI value is viewed as superior because it is simpler and requires fewer parameters. The NNFI can yield negative values and values above 1.O, but generally is interpreted similarly to the NFI. Bonett and Bentler view NFI and NNFI values of .90 and above as indicative of good fit. Hagenaars (1990) suggested the use of the Baysian Information Criterion [BIC, Raftery, 1986; where BIC = G’ - (In N) . (dfl] as a useful index in comparing relative model fit because it is the only index that takes explicit account of both sample size and model complexity. This index indicates the posterior odds of preferring the examined model over the saturated model (i.e.. the model that completely accounts for data variation). Models that have lower values are preferred, with negative values being the most preferred. RESULTS Distribution Test Given that the high-point codes were obtained from four different SDS samples, the similarity of the distribution of these codes across the four samples (college males, college females, high school males, and high school females) was examined. Because some of the cells had values of zero, the typical constant of 0.5 was added to the frequencies of each cell to enable valid statistical examination. A backwards deletion log-linear analysis of the four way cross-classification table [first-letter high-point code x second-letter high-point code x educational status (college vs. high school) X sex (male vs. female)] revealed that the best description of the data was composed of the three three-way interactions and all nested lower order terms: first letter x second letter x sex; first letter x second letter x educational status; and first letter x educational status x sex. The maximum likelihood chi-squared goodness of fit was G’ (36, N = 7505) = 29.98, p = .75, indicating a good fit to the data. Deletion of any terms from this model resulted in a significant goodness of fit statistics, indicating that this was the most parsimonious yet adequate model that could describe data variation. The terms in the accepted model indicated that sex and educational

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status are independently related to the two-letter codes. The term sex x educational status x first letter indicates that educational status and sex interact in accounting for different marginal distributions in the first letter (e.g., the proportion of males with R as the first letter is higher than that for females, especially for high school students). Given the independent relations of sex and educational status with two-letter codes, and the difficulty in interpreting higher order log-linear interactions (Elliott, 1988), we examined each sample separately. Model Testing

The fit indices of the six models by sample are presented in Table 3. As can be seen for all indicators of fit, the circumplex model yielded a poor fit in all five samples, which was expected given the greatly divergent frequencies listed in Table 1. Further, the nested models of symmetry and marginal homogeneity also produced poor fit indices across the samples (with the possible exception of the symmetry model for the SDS college males). Since marginal homogeneity is inherent in both the circumplex and the symmetry models, it could be concluded that the assumption of marginal homogeneity (i.e., equal frequencies across the first and second letter high-point codes) is untenable. The inadequacy of marginal homogeneity accounts for the general failure of the symmetry and circumplex models to fit the data. Thus, it appears that there are crucial marginal or base rate differences in the data that must be taken into account. However, the other three models (quasi-symmetry, quasi-circumplex, and quasi-independence) do not require an exact fit of frequencies, only a proportional fit, and in general these models demonstrated a superior fit to the data over the circumplex, symmetry, and marginal homogeneity models. The quasi-symmetry model yielded the best fit to the data (having nonsignificant G2 values for four of the five samples, and NFI and NNFI values of .99 or 1.00). However, the fit of the quasi-circumplex model was also excellent in each sample (very low, but significant G2 values, and NFI and NNFI values of .95 through .99). There was relatively little difference in the fit of the quasi-symmetry and quasi-circumplex models across the samples. However, the BIC index demonstrated clear superiority of the quasi-circumplex in three of the five samples, only the SDS college females and the DOT samples yielded better BIC values for quasisymmetry. The quasi-circumplex model is a much more parsimonious model than the quasi-symmetry model because the quasi-symmetry model requires estimation of many more parameters (20) than the quasi-circumplex model requires (9). Given (a) the uniformly high values of the fit indices for the quasi-symmetry and quasi-circumplex, (b) the fact that the quasi-circumplex model is similar in fit to, though much more restrictive than, the

RIASEC CIRCUMPLEX

305

TABLE 3 Summary of the Goodness-of-Fit for the Log-Linear Models of the RIASEC High-Point Codes by Sample Model

df

Circumplex Symmetry Marginal homogeneity Quasi-symmetry Quasi-circumplex Quasi-independence

Self-Directed Search college males 26 1214.36 .OO .16 15 79.03 .oo .94 5 63.93 .OO .96 10 15.10 .l? .99 21 67.98 .OO .96 19 421.03 .OO .71

.07 .91 .76 .99 .96 .57

1026.42 - 29.4tl 27.79 -57.18 - 83.81 283.69

Circumplex Symmetry Marginal homogeneity Quasi-symmetry Quasi-circumplex Quasi-independence

Self-Directed Search college females 26 2975.08 .OO .13 15 330.31 .OO .90 5 312.91 .OO .91 10 17.40 .07 .99 21 124.85 .OO .97 19 115.78 .OO .97

.03 .82 .48 .99 .96 .Y6

2784.72 220.53 276.31 -55.78 - ‘8.84 - 73.27

Circumplex Symmetry Marginal homogeneity Quasi-symmetry Quasi-circumplex Quasi-independence

Self-Directed Search high school males 26 2090.92 .OO .08 15 332.10 .oo .85 5 322.96 .OO .85 10 9.14 .45 1.00 21 46.67 .Ol .98 19 203.48 .OO .91

.07 .72 .I4 1.00 .98 .87

1891.lY 216.87 284.55 -~67.68 - 114.65 57.52

school females .OO .12 .OO .90 .oo .90 .19 1.00 .OO .99 .oo .9x

.Ol .X1 .44 1.00 .99 .97

4840.71 451.04 516.33 - 64.3’) -Y6.56 - 32.38

Dictionary of Occupational Titles 26 28017.91 .OO .Oh 15 5742.25 .OO .81 5 5633.57 .OO .81 10 108.68 .04 1.00 21 1166.07 .OO .96 19 3886.22 .OO .x7

.05 .63 .lO .99 .95 .80

27773.49 5601.2-l 5586.57 14.67 068.65 3886.22

Circumplex Symmetry Marginal homogeneity Quasi-symmetry Quasi-circumplex Quasi-independence Circumplex Symmetry Marginal homogeneit:Y Quasi-symmetry Quasi-circumplex Quasi-independence

Self-Directed 26 15 5 10 21 19

G’

Search high 5043.58 568.98 555.34 13.64 67.29 115.87

P

NFI

NNFI

BIC

Note. NFI. normed fit index; NNFI, non-normed fit index: BIC = Baysian Information Criterion.

quasi-symmetry model, (c) the BIC indices favored the quasi-circumplex model, and (d) the greater theoretical utility of the quasi-circumplex over the quasi-symmetry model, we thought that the quasi-circumplex model was the better representation of the data. An examination of the residual

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matrices (i.e., differences obtained when actual data are subtracted from the frequencies generated by the model) of the quasi-circumplex model across all five samples revealed that the magnitude of the residuals was uniformly low and that there appeared to be no pattern present, further indicating the fit of the quasi-circumplex model. Thus, the quasi-symmetry and quasi-circumplex models were the best representations of the covariation of first and second letter high-point codes across the five samples with the quasi-circumplex being the more restrictive, parsimonious, and valuable of the two. It is interesting to note the plausibility of the quasi-independence model for the female samples. The quasi-independence model fit almost as well as the quasi-circumplex model on the female samples, especially the SDS college sample. The quasi-independence model indicates that the frequencies vary randomly once the base rates (marginal frequencies) are taken into account. The quasi-independence model was found to be a poor fit for the male SDS samples. DISCUSSION The results of this study confirm our hypothesis that a quasi-circumplex would provide the best fit of the two letter high-point code data for personality types and work environments, thus supporting Holland’s person-environment structural hypothesis. Although sex and educational differences were found in the distributiou of RIASEC codes, the tests of several rival models demonstrated that the structure of Holland codes for all five samples approximated a quasi-circumplex, but not a circumplex. The lack of marginal homogeneity of high-point codes ruled out the fit of the circumplex model, and accounted for most of the sex and age differences in the distributions. When account was taken of the different endorsement rates of each of the RIASEC types, that is, the marginal totals of first and second letter codes, a circumplex structure (i.e., quasicircumplex) was found to be an adequate representation of the data. This support of the quasi-circumplex as the best representation of the frequencies of two letter high-point codes provides qualified support for the claims of consistency and congruence. Gottfredson et al. (1975) argue that society promotes convergence in personal integration and occupational activities and that this convergence can be demonstrated in the consistency of personality types and occupational environments. We demonstrated that the frequencies hold to the quasi-circumplex. The circumplex, with information about base rates (i.e., the quasi-circumplex), can be used to account for the frequency of types and occupations. After accounting for base rates, the probabilities of all adjacent high-point codes are equal, as are all alternate codes, as are all opposite codes, and the probabilities of all adjacent codes are greater than the probabilities of alternate codes which are greater than the prob-

RIASEC

CIRCUMPLEX

307

abilities of opposite codes. The recognition that there are base rate differences among the types and occupations has long existed (e.g., Prediger. 1977), but this study supports the existence of the circumplex structure underlying the base rate differences as well as the theoretical proposition that certain types are more likely to co-exist. The equivocal results previously obtained with respect to consistency (e.g., Erwin, 1982; Gottfredson, 1977; Latona, 1989; O’Neil, Magoon, & Tracey, 1978; Reuterfors, Schneider, & Overton, 1979) could be attributable to the issue of base rates. Typically, the circumplex, not the quasicircumplex, is assumed in defining consistency. No account is taken of base rates and some unequal high-point codes are unjustly equated as representing identical levels of consistency. Some previous researchers have recognized the effect that different base rates could have on consistency (Rose, 1984; Strahan. 1987), but no attempt was made to use the circumplex structure. In future research, the base rate could be taken into account by multiplying each consistency score by the inverse of the base rate of each of the codes. This procedure would provide an index of consistency that would regect the circumplex while also taking account of base rate differences. Similarly, the presence of the quasi-circumplex adds support to the concept of person-environment congruence. Clearly, having parallel structures enables valid comparison of the fit between the two. Thus the results of this study support the parallel structure that exists in both personality types and occupational environments. There are differences in the frequencies of types and environments but these are attributable to base rates. For example, most of the occupations have R as the first letter of the high-point code. But the underlying structure of personality types and occupational environments is the same once base rates have been taken into account, the circumplex. Holland’s (1985b) recommended congruence indices, the Zener and Schnuelle (1976) and Iachen (1984) indices, provide an index of the extent to which the personality type and the occupation agree. However, neither one takes account of the relations among the RIASEC types and environments imbedded in the circumplex. They are straight agreement indices. An index that includes predictions derived from the quasi-circumplex could prove more useful. Prediger (Mau, Swaney, & Prediger, 1990: Prediger & Vansickle, 1992) has taken an initial step in this area by mapping occupations onto the same structure as personality types. The extent of congruence is thus easily derived as a function of the circumplex structure among the types. In this way, the concept of congruence is much more straight forward and easily grasped by researcher, practitioner, and client alike. This mapping is only valid if the same structure is found for both personality and occupations, and the results of the present study support the similarity of structure. More work using the imbedded cir-

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cumplex structure of both the personality and occupational domains is needed. There were some interesting minor differences in the structures between the males and females. The quasi-circumplex was found to be the most reasonable fit to the data for the male samples, while the relative superiority of this model was less clear for the females. For the female samples, the quasi-circumplex, quasi-symmetry, and quasi-independence models had a similar fit. Our choice of the quasi-circumplex as the best representation of the data was based on the fewer parameters required in this model; the data could be accounted for equally well with a simpler model that contained fewer parameters. Regardless, the plausibility of the quasiindependence model for the females indicated that, after account was taken of the base rates, there was little systematic variation in the highpoint codes. This possibility of random association of the first and second high-point codes after account is taken of base rates for females is probably attributable to the extreme base rate associated with the social type for females (approximately 65% of the females had S as the first letter code), leaving little variation of consequence to be taken into account. The major sex difference generated in the results was the divergent base rates for each type. In the late 1970’s, sex differences in base rate probabilities for inventories that report raw scores such as the SDS were a focus of debate (Holland, 1976; Holland, Gottfredson, & Gottfredson, 1976; Prediger, 1976; Prediger & Cole, 1975; Prediger & Hanson, 1976). Prediger (1977), for example, demonstrated that in examining the validity of RJASEC scores, base rates must be taken into account or erroneous or incomplete conclusions can be reached. In a similar vein, the present study showed that base rates when not controlled can lead to different implications about the structure of personality types for men and women. These male-female structural differences would probably disappear or be less prominent with inventories that adjust RIASEC raw score base rate probabilities. When RIASEC scores are based on same-sex norms, the distributions of high-point codes are more balanced or less skewed and males and females receive similar distributions of high-point codes (Cole & Hanson, 1975; Prediger & Johnson, 1979). Viewing the RIASEC types as forming a circumplex may lead to new ways of studying the relations between vocational interests and personality. The research linking vocational interests to personality has not been conclusive (Hansen, 1984; also see Borgen’s rebuttal, 1986). The relation of the RIASEC circumplex to the major personality dimensions has been hypothesized by Hogan (1983) and, given Holland’s (1985a, p. 15-23) implication that RIASEC types represent aspects of interpersonal behavior, more research that examines the relation of major personality dimensions to the circumplex or research that examines how major personality traits account for the RIASEC circumplex is needed.

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Furthermore, the major circumplex models of personality (e.g., Kiesler, 1983; Leary, 1957; Wiggins, 1979) focus exclusively on the interpersonal realm and Holland’s model could be viewed as potentially describing similar constructs. The results of this study are limited in generalizability to the samples and measures examined. For example, the quasi-circumplex structure may not be supported with RIASEC measures other than the SDS or on other samples. Further the results of this study are restricted only to two letter high-point codes. Examination of the structure of three letter high-point codes still needs to be conducted. The results, however, do lend support for Holland’s model as well as point out the need for continued research using different instruments and norms. REFERENCES Bonett, D. G.. & Bentler, P. M. (1983). Goodness-of-fit procedures for the evaluation and selection of log-linear models. Psychological Bulletin, 93, 149-166. Borgen, F. H. (1986). New approaches to the assessment of interests. In W. B. Walsh B S. H. Osipow (Eds.), Advances in vocational psychology: Vol. 1. The assessment of interests (pp. 83-125). Hillsdale. NJ: Lawrence Erlbaum. Borgen. F. H.. Weiss, D. J.. Tinsley, H. E. A., Dawis, R. V., & Lofquist. L. H. (lY72). Occupational reinforcer patterns: 1. Minneapolis: University of Minnesota, Department of Psychology, Vocational Psychology Research. Clogg, C. C., Eliason, S. R.. & Grego. J. M. (1990). Models for the analysis of change in discrete variables. In A. von Eye (Ed.), Statistical methods in longitudinal research (Vol. 2, pp. 409-442). San Diego, CA: Academic Press. Cole. N. S., & Hanson. G. R. (1971). An analysis of rhe structure of vocational interests (ACT Research Report No. 40). Iowa City: American College Testing Program. Cole, N. S., & Hanson, G. R. (1975). Impact of interest inventories on career choice. In E. E. Diamond (Ed.), Issues of sex bias and sex fairness in career interest measurement (National Institute of Education Report). Washington, DC: U.S. Gov. Printing Office. Dixon, W. I. (Ed.). (1988). BMDP stafistical software manual. Berkeley. CA: Univ. of California Press. Elliott, G. C. (1988). Interpreting higher order interactions in loglinear analysis. Aychological Bulletin, 103, 12 I- 130. Erwin, T. D. (1982). The predictive validity of Holland’s construct of consistency. Journal of Vocational Behavior, 20, 180-192. Fouad. N. A., Cudeck, R., & Hansen, J. C. (1984). Convergent validity of the Spanish and English forms of the Strong-Campbell Interest Inventory for bilingual Hispanic high school students. Journal of Counseling Psychology, 31, 339-348. Gati. I. (1991). The structure of vocational interests. Psychological Bulletin. 109, 309-324. Gottfredson, G. D. (1977). Career stability and redirection in adulthood. Journal of Applied Psychology,

62, 436-445.

Gottfredson. G. D., & Holland, J. L. (1989). Dictionary of Holland occupational codes (2nd ed.). Odessa, FL: Psychological Assessment Resources. Gottfredson, G. D., Holland, J. L., & Gottfredson, L. S. (1975). The relation of vocational aspirations and assessmentsto employment reality. Journal of Vocational Behavior, 7. 135-148. Gottfredson. L. S. (1980). Construct validity of Holland’s occupational typology in terms

310

TRACEY AND ROUNDS

of prestige, census, Department of Labor, and other classification systems. Journal of Applied Psychology, 65, 697-714. Guttman, L. R. (1954). A new approach to factor analysis: The radex. In P. F. Lazarsfeld (Ed.), Murhematicuf thinking in the social sciences (pp. 258-348). New York: Columbia Univ. Press. Hagenaars, J. A. (1990). Categorical longitudinal data. Newbury Park, CA: Sage. Hansen, J. C. (1984). The measurement of vocational interests: Issues and future directions. In S. D. Brown & R. W. Lent (Eds.), Handbook of counseling psychology (pp. 99136). New York: Wiley. Hogan, R. (1983). A socioanalytic theory of personality. In M. M. Page (Ed.), Nebraska symposium on motivation 1982. Personality: Current theory and research (pp. 55-89). Lincoln. NE: Univ. of Nebraska Press. Holland. J. L. (1973). Making vocutional choices: A theory of careers. Englewood Cliffs. NJ: Prentice-Hall. Holland, J. L. (1976). Consistency and raw scores survive another test: A last response to Prediger and his colleagues. Measurement and Evaluation in Guidance, 9, 132-135. Holland, J. L. (1985a). Making vocational choices: A theory of vocational personalities and work environments (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall. Holland, J. L. (1985b). The Self-Directed Search professional manuaf. Odessa, FL: Psychological Assessment Resources. Holland, J. L. (1987). 1987 Manual supplement for the Serf-Directed Search. Odessa, FL: Psychological Assessment Resources. Holland, J. L., & Gottfredson, G. D. (1990). An annotated bibfiogruphy for Holland’s theoN of vocational personalities and work environments. Baltimore, MD: Johns Hopkins Univ. Holland, J. L., & Gottfredson, G. D., & Gottfredson, L. S. (1976). Read our reports and examine the data: A response to Prediger and Cole. Journal of Vocational Behavior, 7, 253-259. Holland, J. L., Vierstein, M. C., Kuo, H., Karweit, N. L., & Blum, Z. D. (1972). A psychological classification of occupations. JSAS Cutafog of Selected Documents in Psychology, 2, 84-85 (Ms. No. 184). Hyland, A. M., & Muchinsky, P. M. (1991). Assessment of the structural validity of Holland’s model with job analysis (PAQ) information. Journal of Applied Psychology, 76, 75-80. Iachen, R. (1984). A measure of agreement for use with the Holland classification system. Journal of Vocational Behavior, 24, 133-141. Kiesler, D. J. (1983). The 1982 interpersonal circle: A taxonomy for complementarity in human transactions. Psychological Review, 90, 185-214. Latona, J. R. (1989). Consistency of Holland code and its relation to persistence in a college major. Journal of Vocational Behavior, 34, 253-265. Leary, T. (1957). Interpersonal diagnosis of personality. New York: Ronald Press. Mau, W., Swaney, K.. & Prediger, D. J. (1990). Mapping career groups on basic interest dimensions. (ACT Research Report No. 7). Iowa City: American College Testing Program. O’Neil, J., Magoon, T., & Tracey, T. (1978). Status of Holland’s investigative personality types and their consistency levels seven years later. Journal of Counseling Psychology, 25, 530-535. Prediger, D. J. (1976). Do raw scores deserve a D minus? A reply to Holland. Measurement and Evufuation in Guidance, 9, 136-138. Prediger, D. J. (1977). Alternatives for validating interest inventories against group membership criteria. Applied Psychological Measurement, 1, 275-280.

RIASEC CIRCUMPLEX

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Prediger, D. J. (1982). Dimensions underlying Holland’s hexagon: Missing link between interests and occupations? Journal of Vocational Behavior, 21, 2.59-287. Prediger, D. J., & Cole, N. S. (1975). It is time to face some issues: A response to Holland. Gottfredson, and Gottfredson. Journal of Vocational Behavior, 7, 261-263. Prediger, D. J., & Hanson, G. R. (1976). A theory of careers encounters sex: Reply to Holland. Journal of Vocutionul Behavior, 8, 359-366. Prediger, D. J.. Johnson, R. W. (1979). Alternatives to sex-resrrictive vocational mrerest assessmenr (ACT Research Report No. 79). Iowa City: American College Testing Program. Prediger, D. J., & Vansickle, T. R. (1992). Locating occupations on Holland’s hexagon: Beyond RIASEC. Journal of Vocational Behavior, 40, 111-128. Raftery. A. E. (1986). Choosing models for cross-classifications. American Sociological Review, 51, 145-146. Reuterfors, D. L., Schneider, L. J., & Overton. T. D. (1979). Academic achievement: An examination of Holland’s congruency, consistency, and differentiation predictors. Journal of Vocational Behavior, 9, 181-189. Rose, R. G. (1984). The use of conditional probabilities in applications of Holland’s theory. Journal of Vocational Behavior. 28, 145-154. Rounds, J. B. (in press). Vocational interests: Evaluating structural hypotheses. In R. V. Dawis & D. Lubinski (Eds.), Assessing individual differences in human behavior: Neu concepts, methods, and findings. Minneapolis: Univ. of Minnesota Press. Rounds, J. B., Shubsachs, A. P. W., Dawis, R. V., & Lofquist, L. (1978). A test of Holland’s environmental formulations. Journul of Applied Psychology, 63, 609-616. Rounds, I. B., Tracey. T. J.. & Hubert, L. (1992). Methods for evaluating vocational interest structural hypotheses. Journal of Vocufionul Behavior. 48, 239-259. Strahan, R. F. (1987). Measures of consistency for Holland-type codes. Journal of Vocarionul Behavior.

31, 37-44.

Toenjes, C. M., & Borgen, F. H. (1974). Validity generalization of Holland’s hexagonal model. Measurement and Evaluation in Guidance, 7, 79-85. Tracey. T. J.. & Rounds, J. (in press). Evaluating Holland’s and Gati’s vocational interest model: A structural meta-analysis. Psychological Bulletin. U.S. Department of Labor (1977). Dictionary of occupufionul rifles (4th ed.). Washington. DC: U.S. Govt. Printing Office. U.S. Department of Labor (1979). Guide for occupurionul exploration. Washington. DC: U.S. Govt. Printing Office. Wickens. T. D. (1989). Multiwuy contingency ruablesunalysis for the social sciences. Hillsdale, NJ: Erlbaum. Wiggins, J. S. (1979). A psychological taxonomy of trait-descriptive terms: The interpersonal domain. Journal of Personality and Social Psychology, 37, 395-412. Zener. T. B., & Schnuelle, L. (1976). Effects of the Self-Directed Search on high school students. Journal of Counseling Psychology, 23, 353-359. Received: November 20. 1991