# Concepts and Coefficients Based on John L. Holland’s Theory of Vocational Choice—Examining the R Package holland

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## Abstract

**:**

## 1. Introduction

## 2. The Present Paper

## 3. Holland’s Theory of Vocational Choice

#### 3.1. Central Assumptions

#### 3.2. Concepts

#### 3.3. Characterizing People and Work Environments Using the RIASEC Dimensions

#### 3.4. Coefficients Based on the RIASEC Model

## 4. The R Package holland

`con_`’, (e.g.,

`con_oneletter_holland()`). The second function area is related to the concept of differentiation, which is currently only covered with the function

`dif_7_holland()`to compute seven different indices for differentiation. The last main function area addresses the so-called calculus hypothesis, according to which the six interest orientations are arranged in the form of a hexagonal structure. The package holland offers, among other functions, three (wrapper) functions, which are directly addressed to the user. Within the calculus hypothesis the arrangement of empirical data can be determined (cf. function

`Circ_emp`) and their fit to the hexagonal structure can be determined (cf. function

`Circ_test`). Furthermore, other construct domains (e.g., Big Five personality) with their dimensions can be projected into the hexagonal structure (cf. Function

`Circ_pro`). These three functions are based on the method of structural equation modeling proposed by Nagy et al. [18] , which was implemented as Mplus syntax. The application of the three functions therefore requires an installation of the commercial software Mplus (cf. also

`MplusAutomation`). In addition to these three core areas, there is also the

`misc`area, which includes various auxiliary functions, and the

`datasets`area, which includes various correlation tables for the RIASEC (captured with the AIST-R [8,9]) and Big Five dimensions.

`install.packages("holland",dependencies = TRUE)`

#### 4.1. Congruence Indices in holland

`con_`’ and have a similar structure with regard to their main function arguments. The first two function arguments always refer to the person code (argument

`a`) and to the environment code (argument

`b`).

`con_oneletter_holland()`and its application in

`R_snippet_001`which returns the one letter congruence index according to Holland [28].

1 library ( holland ) # loads the package ... assuming it is installed 2 con _ oneletter _ holland (a=" RIASEC ",b=" AIRCES ") 3 con _ oneletter _ holland (a=" RIASEC ",b=" AIRCES ",letter = 2) 4 con _ oneletter _ holland (a=" RIASEC ",b=" RIASEC ") 5 con _ oneletter _ holland (a=" RIASEC ",b=" RIASEC ",hexadist = TRUE , letter = 1) 6 con _ oneletter _ holland (a=" RIASEC ",b=" IRASEC ",hexadist = TRUE , letter = 1) 7 con _ oneletter _ holland (a=" RIASEC ",b=" AIRCES ",hexadist = TRUE , letter = 1) 8 con _ oneletter _ holland (a=" RIASEC ",b=" SIRCEA ",hexadist = TRUE , letter = 1)

`letter`’, one can control which letter in the two sequences, with a maximum length of 6 letters, the inference of congruence should be based on (see code line 3). Note that unlike in the other ’classical’ congruence functions, a larger numerical value (in this case 1 vs. 0) stands for miss fit in congruence here. If the argument ’

`hexadist=TRUE`’ is set, this dichotomous congruence statement is extended by a gradual congruence statement whose expression depends on the distance of the respective interest orientation in the hexagonal configuration (see code line 5–8 in

`R_snippet_001`). Algorithmically, this is realized internally by establishing a $6\times 6$ distance matrix for the six RIASEC dimensions, where the values 0 stand in the diagonal and the integer distance values (1, 2, 3) stand with increasing distance from the diagonal, where a 3 stands for a letter combination of dimensions opposite in the hexagon. These distances then flow into the calculation of the Holland one-letter congruence index.

`con_twoletter_holland()`and

`con_threeletter_holland()`works but without the option to consider the hexagonal arrangement (

`hexadist`) of the dimensions of vocational interests. The respective algorithmic basis of the two indices is given in ([two letter code] Healy and Mourton [46]) and ([three letter code] Wolfe and Betz [56]).

`R_snippet_002`.

1 # assuming ’holland ’ is loaded 2 # create a vector of some possible combinations of Holland three - letter codes - 3 person <- apply (( combn (x = c("R","I","A","S","E","C"), m =3)) ,2, paste0 , 4 collapse ="") 5 # create a single environment Holland three - letter code ----------------------- 6 environ <- " RIA " 7 # create a vector of function names to be called for congruence indices ------- 8 func <- c(" con _ hamming _ holland "," con_ levenshtein _ holland "," con _ brown _c_ holland " 9 ,"con _ compindex _ holland ","con _ iachan _ holland "," con _n3_ holland ", 10 " con _zs_ holland ") 11 # apply all functions to all combinations of Holland three - letter codes ------- 12 con _ indices <- sapply (func , function (x){ 13 sapply (person , function (y){do. call ( what = x, args = list (a=y, b= environ ))}) 14 }) 15 # look at the resulting indices for congruence with " RIA " environment code ---- 16 con _ indices

`R_snippet_002`, we apply each of these functions to the vector of the person codes and the single environment code to return a matrix with two plus five columns, one for each congruence index with values for congruence in each row for the person codes respectively (see Table 2).

`con_hamming_holland()`computes the location-weighted, cost-sensitive Hammig distance [61]. The function

`con_levenshtein_holland()`finds the distance according to Levenshtein [62] between two sequences (see, [71]), which are the Holland codes given in argument a, which is the person code, and argument b, which is the environment code. Computational details can be found in Needleman and Wunsch [73].

#### 4.2. Differentiation Indices in holland

`holland`.

`’dif_7_holland’`within the R-package

`holland`. As to call one of these indices one has to specify which index for differentiation to compute by assigning the respective character expression (as listed in the first column in Table 3) to the argument

`’ind’`within the function (e.g.,

`ind = "DI5"`, to compute the differentiation according to [45]). in the subsequent R snippet ’

`R_snippet_003.R`’ we first create data for four possible RIASEC score profiles (see code lines 1–5).

1 # create a matrix with possible interest score profiles : --------------------- 2 SP <- matrix ( data = c(50 ,15 ,15 ,12 ,10 ,10 , 3 50 ,45 ,15 ,14 ,12 ,40 , 4 50 ,48 ,26 ,20 ,14 ,10 , 5 50 ,50 ,50 ,50 ,50 ,50) 6 ,nrow = 4, ncol = 6, byrow = T, dimnames = list (c(" Profile _1"," Profile _2", 7 " Profile _3"," Profile _4"),c("R","I","A","S","E","C"))) 8 # plot the four score profiles : ---------------------------------------------- 9 matplot (x = t(SP),type = "b",pch = " ",xaxt ="n",ylim = c (10 ,50) ,bty ="n", 10 ylab = " raw score ",lty =c (1:4) ) 11 axis ( side = 1,at=c (1:6) ,labels = colnames (SP)) 12 segments (x0 = rep (1 ,5) , y0 = seq (20 ,40 ,10) , x1 = rep (6 ,5) , 13 y1 = seq (20 ,40 ,10) ,col = " gray80 ") 14 segments (x0 = 1:6 , y0 = rep (10 ,6) , x1 = 1:6 , y1 = rep (50 ,6) ,col = " gray80 ") 15 text (x = 1:6 ,y = c(t(SP)), labels = c(t(SP)), cex = .8) 16 legend (1 ,20 , legend = rownames (SP),cex = .7, col = 1:4 , lty =c (1:4) ) 17 # compute differentiation according to Holland (1973) ------------------------ 18 apply (SP , 1, dif _7_ holland , ind = "DI5 ") 19 # compute all of the seven differentiation indices --------------------------- 20 ind <- c(" DI1 "," DI2"," DI3 "," DI4"," DI5 "," DI6 "," DI7 ") 21 sapply (ind , function (x){ apply (SP , 1, dif _7_ holland , ind = x)})

`R_snippet_003.R`’, we now calculate the differentiation according to Holland [45] for all of these four profiles. As expected, this index (“DI5”) cannot distinguish the two profiles 1 and 3 with respect to their differentiation and assigns a value for differentiation of 40 to both (higher values indicate higher differentiation). In order to compare the different ability of the seven indices to discriminate the four score profiles in more detail, we can calculate values for the differentiation according to all seven indices for the four profiles by running code lines 20–21. From the results summarized in Table 4 we see, that the seven indices produce different rankings of the four profiles with regard to their differentiation.

#### 4.3. The Calculus Hypothesis in holland

`Circ_emp()`allows for computing the empirical angular locations of the six interest dimensions based on a full correlation matrix and the respective sample size. Some hints on how to structure such a full correlation matrix are given in some examples, which can be accessed by typing the R command

`data(example1)`or

`data(example2)`. The result of executing this function can be assigned to an related plotting S3 Method to return a graphical visualization of the estimated angular locations. The subsequent R snippet demonstrates how to produce the Figure 2 visualizing some empirical RIASEC correlations initially analyzed by Heine et al. [24].

1 ## assuming ’holland ’ is loaded and Mplus is installed 2 # (re) construct the correlation matrix from Heine , Langmeyer & Tarnai (2011) -- 3 korr <- matrix ( data = c (1.0000 ,0.5411 , -0.0882 , -0.1294 , -0.1329 ,0.1417 ,0.5411 , 4 1.0000 ,0.2105 ,0.0045 , -0.0440 ,0.1047 , -0.0882 ,0.2105 , 5 1.0000 ,0.4593 ,0.1905 ,0.0914 , -0.1294 ,0.0045 ,0.4593 , 6 1.0000 ,0.4692 ,0.2288 , -0.1329 , -0.0440 ,0.1905 ,0.4692 , 7 1.0000 ,0.4540 ,0.1417 ,0.1047 ,0.0914 ,0.2288 ,0.4540 , 8 1.0000) ,nrow = 6, ncol = 6, byrow = F); korr 9 # generate , run and read in results from Mplus code --------------------------- 10 result <- Circ _ emp (N = 734 , Cor = korr , konstrukt = c("R","I","A","S","E","C")) 11 # plot the result object ------------------------------------------------------ 12 plot ( result , lcolor = c(" black "," black "," blue "," blue "),ltype = c(1, 1) ,lwd = 3, 13 defhexa = list ( hexa = TRUE , seg = TRUE , gr = 5, r = 4, nseg = 7, 14 x. cent = 0, y. cent = 0, circle =T) ) 15 # add a grey circle around the hexagon ---------------------------------------- 16 r <- 4.05 17 Hxx <- r*sin ( seq ((0) ,((2*pi)), length . out =360) ) 18 Hyy <- r*cos ( seq ((0) ,((2*pi)), length . out =360) ) 19 lines (Hxx ,Hyy , col =" grey90 ",lty =1, lwd =3)

`Circ_test()`, it is possible to test whether any given full correlation matrix fits to a given (hexagonal) angular arrangement. The given (hexagonal) angle arrangement to be tested against can be specified with the argument

`test`in two different ways. The typical approach is certainly to test whether a given empirical correlation matrix fits the ideal hexagonal structure as postulated in the calculus hypothesis. This is achieved by specifying the argument according to the following expression:

`test="perfect"`, which is also the default setting. In addition, it is possible to test against an arbitrary (hexagonal) angle arrangement by passing the six angles (in RIASEC order) as numerical values in radians to the argument ’

`test`’. The last function

`Circ_pro()`allows for the angular projection of additional dimension into the hexagonal structure of the vocational interest dimensions from (possibly) associated constructs, such as for example the Big Five dimensions of personality. For such a projection of additional construct dimensions, an appropriately populated correlation matrix must be passed to the function. How such a correlation matrix has to be structured can be taken from a corresponding data example, which can be accessed via the R command

`data(example3)`or

`data(example4)`. Finally, the result of the function

`Circ_pro()`can be assigned to an related plotting S3 Method to return a graphical visualization of the estimated angular locations for both, the six RIASEC dimensions, as well as the additional construct dimensions, projected into the hexagon.

#### 4.4. The Functional Area Miscellaneous in holland

`misc`’, a brunch of functions are subsumed, that allow for some convenient data manipulation functionalities. The function

`kormean()`takes the mean of the entries of two correlation matrices using the Fisher-Z transformation of the coefficients in both matrices. The function

`sco2let()`allows for converting RIASEC score profiles to Holland letter-codes. The function

`sim_score_data()`will simulate Person (raw)-scores for an arbitrary number of dimensions (latent variables) assessed with any type of questionnaire given the maximum and minimum raw score for each dimension, and some more functions, just to mention a few important ones. Next to such helper functions there are some internal functions providing a comprehensive plotting environment, which is currently used only by one central plotting function exported to the user. The function

`plot_profile_holland()`basically allows for visualizing a individual interest profile given in the form of six score values, which can either be norm values or raw-scores as returned by a vocational interest inventory such as the AIST–R [8] or the AIST 3 [9]. In the subsequent R-snippet (’

`R_snippet_005`’), we first simulate some data using an empirical correlation matrix (code lines 3–7) from the german AIST female norm sample [8], run some descriptives on the resulting data (code lines 9–11), demonstrate two examples to identify ties when ranking RIASEC score profiles (code lines 13–16), apply a conversion to Holland letter-codes (code lines 18–20), and finally add some of the indices for congruence and differentiation (code lines 22–29) already discussed above.

1 ## assuming ’holland ’ is loaded 2 # get an RIASEC correlation matrix -------------------------------------------- 3 data ( AIST _ 2005 _F_ 1270) 4 # simulate raw scores with minimum = 10 and maximum = 50 ---------------------- 5 set . seed (1234) 6 D <- sim _ score _ data (n =1000 , cormat = AIST _ 2005 _F_1270 , min . score = 10, 7 max . score = 50, data . frame = T) 8 # look at some descriptives --------------------------------------------------- 9 apply (D, 2, range ) 10 apply (D, 2, mean ) 11 apply (D, 2, sd) 12 # add index for ties on the 6 dimensions -------------------------------------- 13 D$ Ties6 <- apply (D, 1, function (x){ length ( unique (x [1:6]) )!= 6}) 14 # add index for ties on three highest dimensions ------------------------------ 15 D$ Ties3 <- apply (D, 1, function (x){ length ( unique (x [1:6][ order (x [1:6] , 16 decreasing = T) [1:3]]) )!= 3}) 17 # add a ( character ) vector of full 6- letter - codes for every person ------------ 18 D$ Letter6 <- apply (D, 1, function (x){ sco2let (x [1:6] , len = 6) }) 19 # add a ( character ) vector of 3- letter - codes for every person ----------------- 20 D$ Letter3 <- apply (D, 1, function (x){ sco2let (x [1:6]) }) 21 # add the ’DI7 ’ index to data set ’D’ ----------------------------------------- 22 D$ DI7 <- apply (D[ ,1:6] , 1, function (x){ dif _7_ holland (A = x, ind = " DI7 ")}) 23 # add the ’Hamming distance ’ index to data set ’D’ ---------------------------- 24 env <- " RIA" 25 D$ hamming <- sapply (D$ Letter3 , function (x){ con _ hamming _ holland (a = x,b = env )}) 26 # add the ’Iachan ’ index to data set ’D’ -------------------------------------- 27 D$ iachan <- sapply (D$ Letter3 , function (x){con _ iachan _ holland (a = x,b = env)}) 28 # add the ’Brown -C’ index to data set ’D’ ------------------------------------- 29 D$ brownc <- sapply (D$ Letter3 , function (x){con _ brown _c_ holland (a = x,b = env )}) 30 head (D,n = 7)

`R_snippet_005`’ results in an output showing the first seven cases in the simulated data set on the R console, as depicted in the box below. Next to the raw scores for each of the six RIASEC dimensions (columns 1–6), there are two index variables pointing to cases with ties on the individual RIASEC rank order (columns 7–8), as well as letter-codes with either a length of six or three letters (columns 9–10), the “DI7” index for differentiation and in the last three columns indices for congruence according to an environment characterized by the code “RIA”.

R I A S E C Ties6 Ties3 Letter6 Letter3 DI7 hamming iachan brownc 1 22 30 36 15 33 32 FALSE FALSE AECIRS AEC 7.234178 2.4375 4 3 2 22 22 24 21 25 21 TRUE FALSE EARISC EAR 1.500000 1.5625 6 8 3 23 28 35 28 28 23 TRUE TRUE AISERC AIS 4.031129 0.7750 9 11 4 28 44 33 27 31 33 TRUE TRUE IACERS IAC 5.557777 1.4375 12 10 5 20 18 30 21 28 22 FALSE FALSE AECSRI AEC 4.336537 2.4375 4 3 6 31 25 23 22 19 21 FALSE FALSE RIASCE RIA 3.818813 0.0000 28 18 7 12 15 27 26 36 21 FALSE FALSE EASCIR EAS 7.987838 1.0875 2 9

`R_snippet_006`’) we first calculate some descriptives for three congruence indices for the simulated data by sub setting the data using the indicator for ties considering the three strongest dimensions (code lines 4–16). We then demonstrate how to plot a circular representation of a score profile. Here we do not aim at plotting individual score profiles, but (mean) aggregated score profiles for the sub sample of cases showing congruence above vs. below the mean of the congruence index distribution respectively (code lines 20–30). These examples show how different samples can be described based on the interests of the respondents. In addition, in this context, the differences in the congruence indices used can be clearly illustrated.

1 ## assuming ’holland ’ is loaded and data ’D’ is present in workspace 2 head (D,n = 7) 3 # calculate means for congruence indices by ties vs no ties ------------------- 4 by( data =D, INDICES =D$Ties3 , function (x){ 5 colMeans (x[,c(" hamming "," iachan "," brownc ")]) 6 }) 7 # calculate standard deviation for congruence indices by ties vs no ties ------ 8 by( data =D, INDICES =D$Ties3 , function (x){ 9 sapply (c(" hamming "," iachan "," brownc "),function (y){ 10 sd(x[,y]) 11 }) 12 }) 13 # calculate correlations between congruence indices by ties vs no ties -------- 14 by( data = D, INDICES = D$Ties3 , function (x){ 15 cor (x[,c(" hamming "," iachan "," brownc ")]) 16 }) 17 # sub setting data restricted to cases without ties on 3 dimensions ----------- 18 D1 <- D[D$ Ties3 == FALSE ,] 19 # calculate score profile means below vs. above mean iachan congruence -------- 20 iac _ UPm <- colMeans (D1[D1$ iachan >= mean (D1$ iachan ) ,1:6]) 21 iac _ LOm <- colMeans (D1[D1$ iachan <= mean (D1$ iachan ) ,1:6]) 22 # plot circular score profile means below vs. above mean iachan congruence ---- 23 plot _ profile _ holland (x=iac _UPm ,ri.M=10 , ro.M=50 , cex .sl =.8 , cex .la =1.4 , circle =T) 24 plot _ profile _ holland (x=iac _LOm ,ri.M=10 , ro.M=50 , cex .sl =.8 , cex .la =1.4 , circle =T) 25 # calculate score profile means below vs. above mean hamming congruence -------- 26 ham _ UPm <- colMeans (D1[D1$ hamming >= mean (D1$ hamming ) ,1:6]) 27 ham _ LOm <- colMeans (D1[D1$ hamming <= mean (D1$ hamming ) ,1:6]) 28 # plot circular score profile means below vs. above mean hamming congruence --- 29 plot _ profile _ holland (x=ham _UPm ,ri.M=10 , ro.M=50 , cex .sl =.8 , cex .la =1.4 , circle =T) 30 plot _ profile _ holland (x=ham _LOm ,ri.M=10 , ro.M=50 , cex .sl =.8 , cex .la =1.4 , circle =T)

`R_snippet_006`’).

**b**and

**d**) for this most congruent sub sample shows that for the Iachan index (panel

**b**) with $V=19.{22}^{\circ}$ a smaller angle is shown than for the Hamming distance (panel

**d**) with $V=33.{39}^{\circ}$. This finding reflects the fact that, as described above, the Iachan index emphasizes the first letter of the 3-letter code more strongly, and thus the mean overall vector approaches the dimension Realistic. Correspondingly, regarding the sub samples of below average congruent cases, the vectors shows in the direction of the Social dimension that is antagonistic to the Realistic dimension. Again, this is more pronounced when the Iachan index is used ($V={171.38}^{\circ}$) instead of the Hamming distance ($V={160.96}^{\circ}$).

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Projection of the RIASEC dimensions into the perfect hexagon based on a sample of a South German University (N = 734) [24].

**Figure 4.**Circular graphical visualizations for mean aggregated interests score profiles with resulting mean interests vector V; upper panel (

**a,b**): Subsamples mean splitted by Iachan [50] index, ((

**a**): bellow mean, $V={171.38}^{\circ}$, (

**b**): above mean, $V={19.22}^{\circ}$); lower panel (

**c,d**): Subsamples mean splitted by Hamming distance [61] index, ((

**c**): above mean, $V={160.96}^{\circ}$, (

**d**): below mean, $V={33.39}^{\circ}$); all values in degree clockwise starting at dimension Realistic.

**Table 1.**Concepts and corresponding coefficients based on Holland’s [1] RIASEC dimensions.

Concept | Profiles | Coefficient |
---|---|---|

Congruence | 1-letter codes | DFLA index [28] |

FLAH [45] | ||

2-letter codes | TLA index [46] | |

3-letter codes | Z-S index [55] | |

TLC index [56] | ||

Compatibility index [57] | ||

RCCS [58] | ||

M index [50] | ||

K-P index [59] | ||

C index [43] | ||

M3 index [47] | ||

N-3 index [51] | ||

Flexible number of letters | Sb index [60] | |

Modified C index [48,49] | ||

Hamming distance [61] | ||

Levenshtein distance [62] | ||

Scores and 3-letter codes | PICS [63] | |

Scores | Polynomial regression [52] | |

Profile correlation [3] | ||

Profile deviance [3] | ||

Euclidean distance [53] | ||

Angular agreement [53] | ||

Consistency | 2-letter codes | Holland’s measure [64] |

Strahan’s measure I [65] | ||

3-letter codes | Strahan’s measure II [65] | |

Scores | R${}^{2}$ (cosine function) [25] | |

Differentiation | Scores | Frantz & Walsh’s measure [66] |

Spokane & Walsh’s measure [67] | ||

Iachan’s measure I [68] | ||

Iachan’s measure II [68] | ||

Holland’s measure [45] | ||

Peiser & Meir’s measure [69] | ||

Healy & Mourton’s measure [46] | ||

Length of interest vector [40] | ||

Amplitude (cosine function) [25] | ||

Interest flexibility | Scores | Sum of scale scores [27] |

**Table 2.**Values for congruence between the single “

**RIA**” environment code and some possible combinations of personal three-letter codes for seven congruence–indices.

Sequence Based Indices | ‘Classical’ Indices | ||||||
---|---|---|---|---|---|---|---|

Hamming ^{g} | Levenshtein ^{f} | Brown–C ^{a} | Comp. ^{b} | Iachan ^{c} | N3 ^{d} | ZS ^{e} | |

RIA | 0.00 | 0.00 | 18 | 8 | 28 | 3 | 6 |

RIS | 0.02 | 0.02 | 17 | 7 | 27 | 2 | 5 |

RIE | 0.50 | 0.37 | 16 | 7 | 27 | 2 | 5 |

RIC | 0.75 | 0.50 | 15 | 7 | 27 | 2 | 5 |

RAS | 0.33 | 0.13 | 15 | 5 | 24 | 2 | 2 |

RAE | 0.81 | 0.37 | 14 | 5 | 24 | 2 | 2 |

RAC | 1.06 | 0.50 | 13 | 5 | 24 | 2 | 2 |

RSE | 1.12 | 0.40 | 12 | 0 | 22 | 1 | 3 |

RSC | 1.37 | 0.52 | 11 | 0 | 22 | 1 | 3 |

REC | 1.68 | 1.00 | 9 | 0 | 22 | 1 | 3 |

IAS | 0.71 | 0.38 | 12 | 4 | 12 | 2 | 2 |

IAE | 1.18 | 0.62 | 11 | 4 | 12 | 2 | 2 |

IAC | 1.43 | 0.75 | 10 | 4 | 12 | 2 | 2 |

ISE | 1.50 | 0.65 | 9 | 3 | 10 | 1 | 1 |

ISC | 1.75 | 0.77 | 8 | 3 | 10 | 1 | 1 |

IEC | 2.06 | 1.12 | 6 | 3 | 10 | 1 | 1 |

ASE | 1.87 | 1.13 | 6 | 2 | 4 | 1 | 1 |

ASC | 2.12 | 1.26 | 5 | 2 | 4 | 1 | 1 |

AEC | 2.43 | 1.50 | 3 | 2 | 4 | 1 | 1 |

SEC | 2.81 | 2.01 | 0 | 0 | 0 | 0 | 0 |

^{a}Brown–C: Index of Congruence according to Brown and Gore [43] ;

^{b}Comp.: Comparative-Index of Congruence according to Wiggins and Moody [57];

^{c}Iachan: Index of Congruence according to Iachan [50];

^{d}N3: Index of Congruence according to Joerin Fux [51];

^{e}ZS: Index of Congruence according to Zener and Schnuelle [55]

^{f}Levenshtein: Sequence based Index according to Levenshtein [62]

^{g}Hamming: Sequence based Index according to Hamming [61].

**Table 3.**Differentiation indices for Holland profiles implemented in the R-package

`holland`as cited in ([7], p. 267).

Index | Brief Description | Author/Source |
---|---|---|

DI1 | Difference between highest and second highest interest score | (Frantz & Walsh, 1972) [66] |

DI2 | Difference between highest and third highest interest score | (Spokane & Walsh, I978) [67] |

DI3 | Difference between highest score and the average of the second and fourth highest score | (Iachan, 1984) [68] |

DI4 | Difference between highest score and the average of the third and fifth highest score | (Iachan, 1984) [68] |

DI5 | Difference between highest and lowest score | (Holland, 1973) [45] |

DI6 | Difference between highest and lowest score, standardized by the overall level of interest | (Peiser & Meir, 1978) [69] |

DI7 | Dispersion of interest scores | (Healy & Mourton, 1983) [46] |

DI1 | DI2 | DI3 | DI4 | DI5 | DI6 | DI7 | |
---|---|---|---|---|---|---|---|

Profile_1 | 35.00 | 35.00 | 36.50 | 37.50 | 40.00 | 0.36 | 14.16 |

Profile_2 | 5.00 | 10.00 | 20.00 | 23.00 | 38.00 | 0.22 | 15.95 |

Profile_3 | 2.00 | 24.00 | 16.00 | 30.00 | 40.00 | 0.24 | 15.66 |

Profile_4 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

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Hartmann, F.G.; Heine, J.-H.; Ertl, B.
Concepts and Coefficients Based on John L. Holland’s Theory of Vocational Choice—Examining the *R* Package *holland*. *Psych* **2021**, *3*, 728-750.
https://doi.org/10.3390/psych3040047

**AMA Style**

Hartmann FG, Heine J-H, Ertl B.
Concepts and Coefficients Based on John L. Holland’s Theory of Vocational Choice—Examining the *R* Package *holland*. *Psych*. 2021; 3(4):728-750.
https://doi.org/10.3390/psych3040047

**Chicago/Turabian Style**

Hartmann, Florian G., Jörg-Henrik Heine, and Bernhard Ertl.
2021. "Concepts and Coefficients Based on John L. Holland’s Theory of Vocational Choice—Examining the *R* Package *holland*" *Psych* 3, no. 4: 728-750.
https://doi.org/10.3390/psych3040047