Human Resource Management Review 18 (2008) 311–321

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Human Resource Management Review

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Person–environment fit or person plus environment: A meta-analysis ofstudies using polynomial regression analysis

Liu-Qin Yang a,⁎, Edward L. Levine a,1, Mark A. Smith b, Dan Ispas a, Michael E. Rossi a

a PCD4118, Department of Psychology, University of South Florida, Tampa, Florida, 33620, USAb Valtera Corporation, Houston, TX, USA

a r t i c l e i n f o

⁎ Corresponding author. PCD4118G, Psychology DepE-mail addresses: lyang2@mail.usf.edu (L.-Q. Yang)

1 Tel.: +1 813 974 0459; fax: +1 813 974 4617.

1053-4822/$ – see front matter © 2008 Elsevier Inc. Adoi:10.1016/j.hrmr.2008.07.014

a b s t r a c t

Keywords:

The purpose of this studywas to examine if the non-linear terms inpolynomial regression analysis(PRA) explain substantial amounts of variance in assumed outcomes over and above the linearterms. This meta-analysis reviewed a total of 30 studies from 25 articles on person–environment(P-E)fit inwhich PRAwas used.We found that none of the 30 studies did rigorous cross-validationfor PRA. In addition, the overall population R2 change attributable to the non-linear terms (PE, P2

and E2) in PRAwas only .008. However, the P-E interaction termmay bemore important in somesituations than in others, based on the data gatheredhere. Specifically, the non-linear terms in PRAadded to the variance explained by the linear terms (P and E) when studies examined assumedoutcome variables like contextual performance or job attitudes as opposed to task performance. Insummary, PRA could potentially be effective in investigating P-E fit and other human resourcemanagement-related phenomena when it is used in appropriate scenarios.

© 2008 Elsevier Inc. All rights reserved.

Person-environment fitPolynomial regression analysisR2 changeNon-linear termsCross-validation

1. Introduction

The degree of fit between people and environments withinwhich they function is a concept that dates back many years in bothpsychology (e.g., Lewin,1935; Murray,1938) and human resourcemanagement (HRM). For instance, in HRM, person–vocation fit isone general way that researchers have considered person–environment (P-E) fit for work situations. Holland's theory of job fit isprobably the best known of these theories (Holland, 1985). It states that people are happier and more successful in their workenvironment when their personality matches characteristics of the environment. As an example, this theory maintains that anartistic person would be most successful in artistic jobs, whereas an investigative person would be most successful in investiga-tive jobs. The key notion is that it is not just the person or the environment that determines success on the job — it is the match orfit between them. As a very general alternative to Holland's theory, one could postulate that certain types of people are generallymore successful (regardless of job) and certain vocations have more successful workers (regardless of the types of people). In thiscase, the person–vocation fit may not be as important as a focus on the people and their vocations.

Researchers have proposed theories and conducted empirical studies dealing with other types of fit including Person–Job (P-J),Person–Group (P-G), Person–Organization (P-O) and Person–Person (P-P) such as person–supervisor fit (e.g., Kristof, 1996; Kristof-Brown, Zimmerman, & Johnson, 2005; Smith & Levine, 2004). Despite the well-known theories of person–environment (P-E) fit,studies testing them have often utilized what are now recognized as inappropriate measures and indicators of fit (Edwards, 1991).Thus, it has been problematic to interpret many of the findings. More recently, researchers have begun to follow therecommendations of Edwards and colleagues (e.g., Edwards & Parry, 1993) who have called for the use of a more complex andappropriate regression model, called polynomial regression analysis (PRA). In the unconstrained PRA model, the relation can be

artment, University of South Florida, Tampa, FL., 33617., elevine@shell.cas.usf.edu (E.L. Levine), msmith@valtera.com (M.A. Smith).

ll rights reserved.

312 L.-Q. Yang et al. / Human Resource Management Review 18 (2008) 311–321

analyzed with the general equation of P (person)+E (environment)+P⁎E+P2+E2. The first of the non-linear terms reflects the jointinfluence of person and environment, i.e., P-E fit.

The purpose of this study is to evaluate the extent towhich the non-linear terms (PE, P2, E2) in the polynomial regression equationadd substantially to the variance explained in outcomes. In other words, does a linear, additive composite of P+E provide a sufficientlycomplete rendering of the influence of these variables on outcomes despite the fact that Edwards and colleagues have shown that it ismathematically appropriate to include non-linear indicators of fit? In essence, the question becomes whether just person and envir-onment are important drivers of assumed outcomes — or whether the fit between person and environment is also important orperhaps evenmore important than the additive, linear combination.We use the term “assumed outcomes” or “assumed effects” sincethe studies included here, and others dealing with fit, are almost invariably correlational in nature and causal relations between theindependent and dependent variables cannot be definitively established (Stone-Romero & Rosopa, 2008).

1.1. Person–environment fit

In a discussion of person–environment fit, it is important to define what is meant by the terms “person” and “environment”.Persons are generally defined by such individual traits as personality, abilities, skills, knowledge, values, goals, or preferences, etc.All individuals can be rated on each of these traits, and they can be used to differentiate between people. Environments, on theother hand, usually refer to some characteristics of the setting and can be rated on such features as size, familiarity, and rewardstructure. In many cases, it is preferable to use the same basic dimensions to measure both people and the environments theyfunction in, such as preferred job autonomy versus autonomy available at work. Some researchers have also proposed thatenvironments can be defined by the traits of the peoplewho are in them (e.g., Holland,1985; Schneider,1987). These theorists haveproposed that researchers can understand and measure an environment by assessing the people in the environment.

It is also important to define the term “fit”, as it can refer to a number of different concepts. Muchinsky and Monahan (1987)noted the crucial difference between supplementary fit and complementary fit. For supplementary fit, a person “supplements,embellishes, or possesses characteristics which are similar to other individuals in an environment (p. 269).” An example of thisinvolves fraternities and sororities, where newcomers often feel that they fit in the organization if they have similar values asothers in the organization. This is a straightforward concept that probably reflects the most common notion of “fit” throughout P-Efit research. On the other hand, complementary fit occurs when a person's characteristics “make whole” the environment or addsome missing element to it. In other words, certain aspects of the environment may fulfill an individual's needs; or, an individualmay have some unique abilities that the environment lacks. Muchinsky andMonahan contend that complementary fit provides thelogic behindmost employment selection decisions. As such, people often are selected for work groups because they possess uniqueskills or abilities that the other group members lack. This treatment suggests that the predicted form of the interaction in PRAwillbe different for each type in that the impact of fit on assumed outcomes of interest will increase at an accelerating rate as bothvariables increase in supplementary fit, but will increase when one of the variables decreases while the other increases incomplementary fit. The prediction of the assumed outcome variable in question will improve in either case when the P⁎Einteraction is significant over and above the weighted linear composite of the P and E measures.

P-E fit can also be considered at various “levels” of work environments (Kristof, 1996). For instance, person–group fit is onewayof considering P-E fit inwork situations, and this refers to the compatibility between an individual and his/her work group or team.Some research has shown that goal, value, or personality similarity of group members positively predicts effective group decision-making (e.g., Klimoski & Jones, 1995). In addition, other research has shown that teams composed of members with diverseknowledge, skills, and abilities (KSA's) are at times more effective than teams where members possess similar KSAs (e.g., Shaw,1981). Person–vocation fit and person–job fit are other ways that researchers have considered P-E fit for work situations. Asmentioned above, Holland's theory of vocational fit is one of the best examples of this (Holland, 1985). Empirical evidence hasshown that person–vocation fit contributes positively to variance in job attitudes and under certain circumstances jobperformance (e.g., Carson & Mowsesian, 1993; Kieffer, Schinka, & Curtiss, 2004).

Another way to consider P-E fit is the match between a person and the organization. P-O fit researchers typically approach fitfrom a supplementary perspective, emphasizing the importance of similar personal and organizational values, or individualpersonality and organizational culture. For instance, a longitudinal study by Chatman (1991) showed that similarity betweenindividual and organizational values predicts job attitudes and turnover. Illustrating the complementary perspective, a study byCable and Judge (1994) found that individuals are differentially attracted to organizations based on their compensation policies.This shows that good P-O fit may also occur when organizations fill the needs of individuals, rather thanwhen they are composedof similar other individuals. In addition, person–supervisor fit (e.g., Glomb & Welch, 2005; Smith & Levine, 2004) and person–coworker fit (e.g., Antonioni & Park, 2001) have been studied. Typically, studies in this area have proposed that similarity betweenindividuals will result in positive relations (Antonioni & Park, 2001). However, some research has shown that differences on keydimensions among individuals could also benefit these work relationships (Glomb & Welch, 2005).

It is also important to note the different assumed outcomes of P-E fit at work that have been proposed and studied. Often jobattitudes have been the focal dependent variables in studies of P-E fit (e.g. Edwards & Rothbard, 1999; Kristof-Brown & Stevens,2001; Ostroff, Shinn, & Kinicki, 2005). For instance, researchers have hypothesized that better fit with your jobmight make you likeyour job better; i.e., enhance your job satisfaction. In addition, overall well-being, task performance, and contextual performance(or organizational citizenship behavior; Organ, 1997), have all been researched. To be specific, the P-E fit literature generallysuggests that higher P-E fit contributes to variance in positive employee well-being, better task performance and more contextualperformance (e.g., Edwards & Rothbard, 1999; Kristof-Brown & Stevens, 2001; Slocombe & Bluedorn, 1999).

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1.2. Measuring person–environment fit

When conducting research on P-E fit, there are a number of measurement issues to consider. One involves the difference betweendirectlymeasured perceptions of fit, and indirectly assessedmeasures of fit (Kristof,1996).Directmeasures of fit involve asking peopleabout whether or not they believe that a good fit exists, so this is an individual's judgment about fit. Research has shown that thesejudgments are highly related to job-related attitudes (e.g., job satisfaction). Edwards (1991) criticized these direct measures,highlighting the fact that they confound the independent effects of the person and the environment with their joint effect. Also, thesemeasures are inherently biased by human perception (Caplan, 1987). On the other hand, indirect assessments of fit allow estimates ofthe independent effects of person and environment, as well as the interaction between the two entities. Until the 1990s, studies ofindirectfit typically operationalized this concept by combining twoormore differentmeasures into a single index (Edwards,1994). Forinstance, many studies of job satisfaction have used the algebraic difference between actual and desired job attributes tomeasure “fit”(Fit=X−Y; Edwards, 1991). Also, the absolute values of difference scores and squared difference scores have been used to assess fit.Other measurement options have included assessments of profile similarity by using the sum of absolute differences, the sum ofsquared differences, and the square root of the sum of the squared differences. Despite their attractive simplicity, these proceduresseem to have major analytical flaws—flaws that have been well explicated by Edwards (1994) and Johns (1981). For example, theseindices conceal the independent and direct effects that each component can have on the outcomes.

Further, these indices are often given credit for predicting more variance than is possible. We do not reiterate the full scope ofthe potential flaws, since Edwards (1994) has done so in a definitive and comprehensive fashion. These flaws have led to thedevelopment of an improved method that relies on a more elegant assessment of fit.

1.2.1. Polynomial regression analysisIn contrast to traditional indices of congruence, Edwards (1994) recommends the use of polynomial regression analysis (PRA).

He justifies this approach by showing that this general quadratic equation can best represent the effects of congruence in mostcases: Z=C0+C1X+C2Y+C3XY+C4X2+C5Y2+e (this can also be called the “unconstrained” model, as it includes all of the possiblequadratic dimensions). This equation shows that themain effect of each variable (X and Y), and the non-linear effect of all variables(XY, X2 and Y2) should all be considered when predicting an assumed outcome. The general PRA equation allows a substantiallymore realistic model of the data than the traditional indices, and each component can be interpreted relatively independently.Because of all the relevant components in each regression equation, PRA allows researchers to predict more variance thantraditional “fit” indices. For instance, one study found that PRA explained 20% more variance than difference scores (Bretz & Judge,1994). It should also be noted that PRA is very similar to the regression technique that is used to analyze moderators (e.g., Aiken &West, 1991). The interaction term (XY) is the key when considering this type of moderator relation and the interaction (cross-product) term represents most researchers' understanding of P-E fit.

Despite the importance of the cross-product scores, it is also important to include the other two non-linear effects (P2 and E2) inthe regression equation. These terms allow researchers to determine if an apparent interaction effect is actually a curvilinear effectof one or both components. For instance, Edwards and Parry (1993) re-analyzed data from a number of previous studies of person–environment fit and found that complex curvilinear relation, indexed by the quadratic terms, were common.

Based on all of this information, PRA appears to be an appropriateway to analyze congruence data. However, evenwith its positivequalities, PRA has somedrawbacks (Edwards,1993). One is that it requires relatively large samples, asmany termsmust be included ineach polynomial regression equation. Further, multicollinearity may be a problem when many related terms are used in the sameregression equation (e.g.,X,XY, andX2), and this can hide important statistical effects (Kristof,1996). Also, it is somewhat unclear aboutthe best way to use this technique with multiple dimensions onwhich P-E fit is considered. If all dimensions are entered into a singleregression equation, statistical power will be reduced because of the loss of degrees of freedom. However, if each dimension isconsidered separately, a large number of significance tests will have to be done, which may increase Type I errors.

Another important problem concerns the interpretation of results. Because many of the terms in the regression equation arecurvilinear or interactive, they require complex procedures for interpretation. For instance, response surface methodology (Box &Draper, 1987) is a common way to present the results (e.g., Edwards & Parry, 1993) in a three-dimensional way. However, thesecomplex procedures for interpretation may be confusing for unfamiliar audiences. In addition, it may be unclear how all of theregression terms in PRA measure the extent of fit — especially the non-linear terms. A final potential problem in using thistechnique is the degree to which measurement of the variables (i.e., P and E) attains a sufficient level of psychometric quality sothat results are robust. All these drawbacks suggest potential fragility in the data and the need to cross-validate or replicate resultsobserved in P-E fit studies using PRA. Aside from the issue of insuring validity of these complex regression equations replication is ahallmark of any scientific enterprise. Thus an important concern becomes whether results of PRA have been replicated or cross-validated in past research.

Given the coexistence of the pros and cons of PRA discussed above, an integrative quantitative review (meta-analysis) of PRAused in P-E fit area is imperative for researchers to gain a better understanding of the complexities of using this approach and ofwhat definitive conclusions, if any, may be drawn regarding its utility.

1.3. Combining previous research results

In the past few decades, meta-analysis has become widely accepted in the social sciences as a useful research method toquantitatively combine the results of a collection of studies on a single topic (Cooper & Hedges, 1994; Hedges & Olkin,1985; Hunter

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& Schmidt, 2004). Inmost cases, meta-analyses have three general goals: (a) to estimate an overall (normally some kind of average)index about the magnitude of the studied relation, along with a confidence interval around the overall effect size index and itsstatistical significance, (b) to test whether the focal relation is homogeneous across studies, and (c) to identify possible moderatorvariables affecting the results, if there is no homogeneity among studies.

Recently, Kristof-Brown, Zimmerman, et al. (2005) conducted a meta-analysis about the relation between different types of fitand various assumed outcomes in the workplace. Specifically, they examined person–job fit, person–organization fit, person–group fit, and person–person fit (e.g., person–supervisor fit). In general, they found that these different types of fit were quitedifferent from each other and that fit predicted both individual behaviors and attitudes. However, it is important to note that thecurrent research is a substantial extension of the previous meta-analysis, as the study by Kristof-Brown, Zimmerman et al.quantitatively aggregated all studies on P-E fit except for those using polynomial regression analyses because this analytic strategywas not congruent with that of the studies they focused on. For those studies they located that relied upon PRA, they described theresults in a qualitative manner. Thus, the current research is designed to pick up where this previous meta-analysis left off.Moreover the focus is not on the establishment of conclusions about substantive relations between P-E fit and specific outcomes,but rather on the utility of the more elegant approach exemplified by PRA.

1.4. Current research

Three key questions were investigated in our meta-analysis. First, have results using PRA been routinely cross-validated orreplicated to insure their robustness? Second, do the non-linear terms in PRA add sufficiently to the additive combination of P+E inpredicting assumed outcomes? One might even conceive of meta-analytic data bearing on this question as a test of Lewin's (1935)classic formulation of B= f (P, E) vs. Murray's (1938) interactive view where B= f (P⁎E) more explicitly formulated the interaction ofthe person and the environment. Finally, what situational factors, if any, might influence the extent towhich these non-linear termssubstantially enhance variance accounted for in predicting outcomes? To address these questions we conducted a meta-analysis ofP-E fit studies that used PRA. In addressing these questions throughmeta-analysis, we hasten to add thatwe are not questioning themathematical appropriateness of PRA, for which a strong case has been advanced and been accepted in the discipline.

2. Method

2.1. Literature search

To identify all possible studies that used polynomial regression analysis to investigate P-E fit topic, we searched two onlinedatabases, PsycINFOandDissertationAbstracts International for peer reviewed journal articles anddissertations, respectively, usingthe keywords Person–Environment Fit and Polynomial Regression Analysis. Only articles and dissertations published between 1994and 2007 were searched. The year 1994 was chosen as the earliest date of interest because it was in 1994 that Edwards publishedhis first peer reviewed article about PRA. Potential conference papers were also searched in the annual conference programs of theSociety for Industrial andOrganizational PsychologyandAcademyofManagement in the past 5 years. The same twokeywordswereused for that search. In addition, we referred to themeta-analysis by Kristof-Brown, Barrick, and Stevens (2005) and Kristof-Brown,Zimmerman, et al. (2005), back-searched eligible articles' reference list, and contacted major researchers in this area.

2.2. Inclusion criteria

Three inclusion criteria were used for this meta-analysis. First, the studies must have focused on P-E fit. Specifically, P indicatespersonal ability, personality, goals, values, value preference, needs, or other preferences, while E indicates environmental demands,conditions, supplies or characteristics corresponding to the person's. Second, Edwards's PRAmethodmust have been used for dataanalysis. Finally, regression table (s) was (were) available or available after contacting the author (s). Specifically, the total R2 of thefull model (with all five terms as P, E, P⁎E, P2, and E2), R2of the reduced model (only linear terms as P and E) and R2 change (thedifference between the above two R2s, our effect size) must have been available. Our preliminary screen identified 32 candidatearticles; i.e., 40 candidate studies. However, 7 of the 32 articles (i.e., 10 studies) were excluded either because we could not reachthe author(s) for further information on the effect sizewe required, or because the author(s) confirmed that their study had seriousflaws, or their data were not retrievable.

The final sample consisted of 25 articles with 30 studies (samples), which included 257 regression equations and yielded a totalsample size of 14,787. More than one effect size was drawn from each of the studies because more than one regression equationwas normally included in each study. For example, a study on the relation between P-J fit in polychronicity and assumed workoutcomes may include four regression equations with four different assumed outcome variables (e.g., job satisfaction, positiveaffect, negative affect and self-efficacy) regressed on P-J fit (e.g., Hecht & Allen, 2005), a subtype of P-E fit.

2.3. Coding and inter-rater reliability

Two of the present study's authors independently coded the study characteristics of 14 studies from 11 articles separately(approximately 45%of the total 30 studies). Researchdesign (cross-sectional, time-lagged, or longitudinal design), sample size, source ofsample (from theU.S. vs. fromother countries), status of cross-validation (yes or no), sample type (employee vs. studentvs. combination

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of both employees and students), publication status (published vs. unpublished), type of fit (person–job fit, person–organization fit,person–group fit and person–person fit), type of assumed outcomes (job attitudes, well-being, task performance, contextualperformance, and others includingmiscellaneous variables such as self-efficacyor trust) andR2 change (the keyeffect size)were coded.

The inter-rater reliabilities of the categorical variables – research design, source of sample, status of cross-validation (yes or no),sample type, and publication status, type of fit and type of outcomes –were calculated using Kappa. The inter-rater reliabilities ofthe continuous variables – sample size and R2 change – were calculated using intra-class correlation coefficients (i.e., ICC(2,1) andICC(3,1); Shrout & Fleiss,1979). The Kappas were all above .9 except for the coding for “source of sample (.86)”, and the ICCs were allabove .99. Discrepancies among coders were resolved via discussion. In short, all the 30 studies were coded by one coder and 14 ofthem were coded independently by another coder to assess inter-rater reliability.

2.4. Procedure

Alf and Graf's (1999) algorithm and Hedges and Vevea's (1998) algorithmwere integrated to estimate the weighted (population)mean R2 change, the confidence interval, and the credibility interval. Specifically, therewere six steps in the analysis. First, a study-levelR2 changewas derived by averaging all the R2 changes of regression equationswithin one study (sample). The study-level effect size (R2

change) is the focus of ourmeta-analysis because individualR2 changes from the regressionmodels usinga single sample are dependentandmay bias parameter estimates (Lipsey &Wilson, 2001). Second, a study-level variance of the distribution of R2 changewas derivedby using average R2 for the full regressionmodels (with P, E, PE, P2 and E2) and average R2 for the reducedmodels (only with P and E) ofeach study, based upon Alf and Graf's (1999) derivation (see Formula 1). The reason is that some R2 changes from certain regressionanalyses were zero, which could lead to the variance (of R2 change) estimates as zero and then bias weighted estimates. This problem,however, can be avoided by averaging R2 for full regression models (with P, E, PE, P2 and E2) and R2 for reduced models (only with Pand E). Third, a study-level weight was derived by taking the inverse of the variance of R2 change for each study. Fourth, the weightedmean R2 change across studies was estimated as the population R2 change by using the study-level R2 changes and weights. Fifth, thestandard deviation (and variance) of the distribution of all study-level R2 changes across studies was derived by taking the inverse ofthe total of all the study-level weights, and so the confidence interval of the population R2 change was estimated accordingly. Finally,Hedges and Vevea's (1998) algorithmwas used to estimate the standard error (i.e., Tau) of the distribution of population R2 change andthe credibility interval of population R2 change by using the study-level mean R2 changes and the study-level weights.

Var R2OA−R

2OB

� � ¼ 4R2OA 1−R2

OA

� �2=nþ 4R2

OB 1−R2OB

� �2=n−8ROAROB :5 2RAB−ROAROBð Þ 1−R2

OA−R2OB−R

2AB

� �þ R3AB

� �=n ð1Þ

indicates the R2 of the full regression model with P, E, P⁎E, P2 and E2. R2OB indicates the R2 of the reduced regression model

R2OAwith only P and E. Accordingly, ROA and ROB indicate the multiple regression coefficients (the square roots of the correspondingR2s). Finally, RAB is defined as the ratio of ROB over ROA, and n denotes the sample size of the regression equation.

In addition, the average R2 of the reduced model was calculated (as a referent to the average R2 change) for each level of eachmoderator through two steps: First, the weighted average of the semipartial Rs (square root of R2) was derived with sample size ofeach study as the weight; second, the average R was converted back to R2, the original metric (Hunter & Schmidt, 2004).

2.4.1. Moderator analysisResearch design, source of sample, sample type, publication status, type of fit and type of assumed outcomes were explored as

potential moderators in this meta-analysis. Hedges and Olkin's (1985) Q-tests of homogeneity were computed to test for potentialmoderating effects.

3. Results

3.1. Study Characteristics

Overall, 30 studies (samples) from25 articles were included in ourmeta-analysis, with a total of 14,787 participants. Twenty-threeof them were published in peer-reviewed journals and seven were unpublished dissertation or conference presentations. Eighteenused samples fromtheU.S.,whereas12of themused samples fromother countries. Employee sampleswereused in25 studies, studentsamples were used in three studies and both employees and students were used in two studies. Twenty-three of them used a cross-sectional design, five used a time-lagged design, and two used a longitudinal design. Nine studies investigated person–job fit, 12 ofthem examined person–organization fit, four of them looked at person–group fit, six studies investigated person–person fit and oneexamined person–occupation fit, with a total of 32 studies in this case due to the fact of one study looking at P-J, P-O and P-G fit withone sample. Twenty-five studies used job attitudes as dependent variables, 14 used well-being (e.g., depression, anxiety or physicalwell-being), six used task performance, four examined at contextual performance (e.g., organizational citizenship behavior) and eightstudies examined other assumed outcome variables (e.g., counterproductive work behavior, or actual turnover).

3.2. Cross-validating results using PRA

Given the potential flaws in PRA discussed above, it is important for empirical studies to cross-validate their results using PRAwith more than one independent sample. Specifically, the PRA regression model (equation) from one sample should be used to

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predict the parallel assumed outcome variables in another independent sample and get the cross-validated overall R2 of PRAmodels and the R2 increment for the three non-linear terms. The cross-validated overall R2 of PRA models and R2 changeattributable to the three non-linear terms should allow more definitive conclusions and be a more rigorous demonstration of theprediction of fit for assumed work outcomes than that from one single sample. However, none of the 25 articles (30 studies)included in our meta-analysis performed a cross-validation of their regression analysis. One thing to note is that four studies usedtwo or three independent samples to test the same hypotheses with PRA separately and got inconsistent results across samples(Hecht & Allen, 2005; Kristof-Brown, Barrick, et al., 2005; Livingstone, Nelson, & Barr, 1997; Smith & Levine, 2004).

3.3. Overall analysis and moderating analysis

As noted above, the approach with Alf and Graf's (1999) algorithm and Hedges and Vevea's (1998) algorithm combined wasused to do both the overall analysis and the moderator analysis. Table 1 presents the results. One important thing to note whileinterpreting the results is that the confidence interval of R2 change from the reduced models (with only P and E) to the full models(with P, E, PE, P2 and E2) could possibly include negative values due to reduced statistical power after adding the three non-linearterms to themodel, and also due to the assumption of normal distribution underlying the concept of confidence interval (i.e., Meanplus or minus 1.96 times Standard Error).

As shown in Table 1, the overall estimated mean R2 change attributable to the non-linear terms across all 30 samples was .008and its confidence interval (CI) included zero, which indicates that this average R2 change was not significantly different from zero.Moreover, this is substantially smaller than the variance explained using only the linear terms, which accounted for an R2 of .096overall. TheHedges'sQ did not provide evidence for the existence of potential moderators (pN .05) perhaps due to the fact that theQstatistics has less statistical power in dealing with unique effect size (R2 change). However, the credibility interval included zero,which suggests the potential existence of moderators to differentiate different levels of R2 change under different circumstances

Table 1Meta-analytic results for the R2 change attributable to the non-linear regression terms of PRA

K N Average R2

(Reducedmodel)

Average R2

changeSE 95% CI Hedges'

QREVC 95% CR

Lower Upper Lower a Upper

Overall 30 14787 .096 .008 .015 − .022 .038 37.71 .005 0 .017

Research designCross-sectional 25 11741 .067 .010 .021 − .031 .050 24.666 .002 .006 .013Time-lagged 3 1213 .065 .022 .054 − .083 .128 2.116 .004 .015 .029Combined b 5 3046 .204 .004 .029 − .052 .061 8.940 .013 0 .022

Source of sampleU.S. sample 20 11116 .102 .007 .017 − .027 .042 33.498 ⁎ .007 0 .021Non-U.S. sample 10 3671 .075 .010 .033 − .055 .076 3.391 0 .010 .010

Sample typeEmployee 24 13389 .096 .008 .016 − .024 .040 34.872 0.006 0 0.019Others c 6 1398 .095 .012 .047 − .081 .104 2.132 0 .012 .012

Publication statusPublished 23 11932 .099 .006 .019 − .031 .043 28.456 .005 0 0.015Unpublished 7 2855 .063 .012 .041 − .069 .093 .482 0 .012 .012

Type of fit d

Person-Job fit 9 4380 .051 .012 .031 − .049 .074 12.509 .008 0 .029Person-Organization fit 12 4311 .099 .010 .028 − .046 .066 8.972 0 .010 .010Person-Group fit 4 1809 .043 .008 .045 − .081 .097 2.318 0 .008 .008Person-Person fit 6 4287 .024 .005 .027 − .049 .057 5.545 .002 0 .008

Outcome variablesJob attitudes 25 10476 .093 .013 .002 .009 .017 33.786 .0067 0 .026Well-being 14 6518 .045 .009 .003 .004 .015 12.591 0 .009 .009Task performance 6 3283 .219 e .004 .002 0 .008 8.469 .010 0 .023Contextual Performance 4 1998 .028 .028 .007 .014 .042 5.304 .013 .002 .054Other outcomes 7 2900 .043 .024 .004 .017 .032 8.727 .011 .002 .046

Note: SE=standard error; CI=confidence interval of average R2 change; REVC=random-effect variance component; CR=credibility interval of average R2 change.a “0” in this column indicates either negative value or value smaller than .001.b It includes all studies using time-lagged or longitudinal design.c It includes studies using students as participants and studies using both employees and students as participants.d The study on Person–Vocation fit was not included because only one study cannot well represent one level of moderating analysis.e This average for the R2 of the reduced model only included five studies with Dabos and Rousseau's (2004) study excluded due to its inclusion of demographic

variables as control variables in the reduced model which was different from the other five studies in this category.⁎ p; .05.

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(Hunter, Schmidt, & Jackson, 1982). Therefore, a few moderator variables were explored based upon the P-E fit literature (e.g.,Kristof-Brown, Barrick, et al., 2005; Kristof-Brown, Zimmerman, et al., 2005) and that of meta-analysis: Research design, source ofsample, sample type, publication status, type of fit and type of outcomes. For each level of themoderators, bothweighted average R2

change and average R2 of the reduced model (with only linear regression terms) are provided in Table 1.Table 1 indicates that studies using a time-lagged design seem to have a higher R2 change attributable to the three non-linear

regression terms in PRA than those using other designs. However, the average R2 change for studies with any of the three studydesigns was not significantly different from zero in that their CIs included zero. T-tests of studies using a cross-sectional designversus those using time-lagged design or all studies using non-cross-sectional design suggested a non-significant moderator effectof study design, t (26)=− .38, pN .05; t (28)=−2.00, pN .05. ANOVA was not used in this case to test the differences across the threedesign groups because therewere only two studies in the longitudinal-design group. Further, there did not seem to be evidence forthemoderating effect of source of sample (i.e., fromU.S. versus fromother countries) and sample type (i.e., employees versus others)based on a t-test, t (28)=1.21, pN .05; t (28)=1.11, pN .05, but the Q-test for the studies using the U.S. samples was significant,indicating the necessity of doing further moderator analysis of those 20 studies. Interestingly, unpublished papers had a slightlyhigher average R2 change attributable to the non-linear regression terms in PRA than those published, and the variance of R2 changewas larger aswell which indicatedmore heterogeneity. Despite this, neither average R2 changewas significantly different from zerobecause their CIs included zero, and a t-test confirmed that there was not a significant difference between these two groups ofstudies, t (28)= .31, pN .05. Therefore, we did not find evidence for the existence of publication bias in our meta-analysis.

With regard to the moderating effect of types of fit, studies on P-J fit seemed to demonstrate the highest average R2 changeattributable to the non-linear regression terms in PRA, those on P-P fit had the lowest average R2 change, whereas those on P-O andP-G fit had average R2 change in between. However, none of the average R2 changes was significantly different from zero andfurther ANOVA analysis did not demonstrate significant results, F (3, 27)= .88, pN .05, for the effect size comparison across the fourtypes of fit. Accordingly, types of fit showed a weak moderator effect.

Finally, when it comes to different assumed outcome variables, all the average R2 changes were higher than zero given thattheir CIs excluded zero except for that for task performance. Studies investigating contextual performance and job attitudesseemed to have higher average R2 changes attributable to non-linear terms than those examining task performance as an assumedoutcome variable, whereas the studies focusing on well-being as an assumed outcome fell in between. The reason is that the CI ofaverage R2 change for contextual performance and that for job attitudes were higher than that of task performance without anyoverlap. Although the regression analysis in the category of studies investigating other assumed outcomes (e.g., turnover,counterproductive work behavior) seemed to have noticeable R2 changes as well, we do not interpret these data because of theircharacteristics of miscellaneousness. Fig. 1 shows the potential moderating effect of assumed outcome variables as a complementto Table 1. However, it is important to note that further ANOVA analysis did not provide evidence of an overall moderator effect oftypes of assumed outcomes, F (4, 51)= .76, pN .05, although the small number of studies per categorymay have limited the power ofthe ANOVA analysis. In short, this moderator effect needs to be viewed cautiously.

Overall, the average R2 change attributable to the three non-linear terms in PRA across our 30 samples was marginal. Studydesign, type of fit (study topic) and type of assumed outcome variables seemed to moderate the strength of the effect size attributeto the non-linear terms in PRA. The pattern of R2 changes across different moderator levels was consistent in terms of both theabsolute values of these R2 changes and the comparisons of them with the R2 of the linear model (baseline). However, in no casedid the effect sizes for non-linear terms attain a magnitude that could be characterized as substantial (medium or large), nor didthey add substantially to predictive efficiency achieved by the linear terms alone, with the possible exception of studies dealingwith contextual performance. In that particular case, however, the small number of studies suggests caution in drawing strongconclusions.

Fig. 1. Different assumed outcome variables and R2 change. Note: CI indicates “confidence interval.”

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4. Discussion

The results of our meta-analysis of 30 studies on P-E fit show that the overall average R2 change for the non-linear terms wasnot significantly different from zero. This outcome may reflect the relative lack of a substantial contribution of non-linear fit termsin PRA to the prediction of presumed outcomes i.e., a low effect size. However, it is important to recognize that there are amultitude of other reasons why moderator variables may fail to be detected. Stone-Romero and Liakhovitski (2002) describedthese in detail. For example, the power of detecting moderator effects could be rather low due to various factors such as smallsample sizes (i.e., small number of studies in our case), restriction of range in predictors, assumed outcomes, or both variables,inadequate scaling of measured variables or the proportion of cases in subgroups of the moderators (Stone-Romero & Liakhovitski,2002). Therefore, moderator effects may be masked or undetected. The implication is that it may not be the lack of contribution offit to the prediction of assumed outcomes that is the problem but rather our presumed inability to detect these contributions giventhe current state of research and measurement. Our data do not permit a conclusion on which explanation is more likely.

However, our meta-analytic search for moderators offered some potential signposts that might raise the feasibility of detectingthe influence of fit in particular circumstances. Specifically, the non-linear terms in PRA may add relatively more to the varianceexplained in outcomes over and above linear regressionwhen studies focus on contextual performance or job attitudes as assumedoutcome variables, as opposed to examining task performance. However, in virtually all cases (i.e., all levels of differentmoderators),with the possible exception of studies of contextual performance, the addition of the non-linear terms does not enhance predictiveefficiency substantially.

4.1. Cross-validating results using PRA

As discussed above, none of the 30 studies included in our meta-analysis performed rigorous cross-validation for PRA. This is aserious concern given the complexity of the regression approach and its susceptibility to bias due to the multicollinearity of theregression terms and often inadequate measurement of P and E variables. Although only four of 25 articles tried to test theirhypotheses with more than one independent sample via PRA, no consistency was observed. It is imperative for future studies tocross-validate results from PRA while investigating P-E fit.

4.2. The incremental predictive validity of adding the non-linear terms in PRA

Overall, the population R2 change for the non-linear termswas .008 based upon the 30 studieswe included in themeta-analysis.This value included zero in its confidence interval despite potential publication bias and capitalization on chance of empiricalstudies included (i.e., fishing expeditions where researchers explore quite a few different regression models before deciding whichto report in their manuscripts). Both publication bias and capitalizing on chancewould theoretically make these R2 results inflated,and yet the average result is still close to zero. This level of incremental validity contributed by the three non-linear terms did notseem to be notable for researchers who are interested in using PRA in their research on P-E fit. With large enough samples, thisamount of R2 change can still be statistically significant. However, wemay ponder whether it is adequate to use such a complicatedapproach to gain suchmarginal incremental validity in explaining variance in assumed outcome variables.Werewe to consider ourdata a test of one interpretation of Lewin's formulation (B= f (P, E)) versusMurray's (B= f (P⁎E)), the data clearly favor the former. Onthe other hand, we may wonder under what situations using PRA can add sufficiently to the variance explained in outcomevariables over and above linear regression to justify the inclusion of the non-linear terms. Although our views on this issue may behelpful in guiding future research, we caution that data at hand are insufficient to permit definitive conclusions.

4.3. When to use PRA?

As discussed above, PRA seemed to demonstrate a greater advantage over linear regressionwhen the studies used a time-laggeddesign, as opposed to either a cross-sectional or a longitudinal design, although the evidence was not strong. It will be interesting toinvestigate the underlying mechanisms behind study design through which the non-linear terms contribute to predicting attitudesand behaviors under such circumstances, especially to the point when the number of time-lagged or longitudinal studies which usePRA is comparable with that of cross-sectional studies. For example, it is possible that the P-E fit dynamics change over time and thechange triggers employees' self-selectionprocess (i.e., “fit” then stay; “misfit” then leave after awhile), which can be related to possiblydifferent levels of effect size (R2 change) attributable to different study designs with different time frames.

When it comes to different types of fit, there seemed to be some evidence for the differential incremental validity of the threenon-linear terms in PRA over and above linear regression, with effect size highest for P-J fit, lowest for P-P fit and in the middle forP-O and P-G fit. However, again, the evidence for the moderator effect was relatively weak. Future studies could focus on possiblydifferent mechanisms through which different types of P-E fit may function then contribute to certain levels of effect size (R2

change) in PRA. For instance, the nature of fit (complementary versus supplementary fit) or themeasurement of fit may account fora unique level of importance of non-linear PRA regression terms in explaining assumedwork outcomes for a certain type of P-E fit.This echoes Kristof-Brown's argument (1996) that different types of P-E fit possibly function in different ways in terms of relating toattitudes and behaviors at work.

Finally, we found some evidence for the differential contribution added by the three non-linear terms in PRA over and above thelinear regression when different assumed outcome variables were chosen in the research on P-E fit. That is, PRA showed the most

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advantage over linear regression when contextual performance or job attitudes were investigated as an assumed outcome,whereas it demonstrated the least advantage when task performance was examined. The incremental validity of the non-linearterms of PRA was in the middle when it came to the assumed outcome of well-being. Two possible explanations can be proposedfor the above results. First, in almost all the cases, perceived fit (self-perceived P and E characteristics separately) instead ofobjective fit (other-observed/archival P and E characteristics separately) was measured, which may explain the strongerassociation between P-E interactions with subjective (self-reported) measures of outcomes like attitudes and contextualperformance, than with relatively objective (or other-reported) measure of task performance.

Second, the differentiation between the supply-value fit (i.e., environment supplies vs. individual values, S-V fit) and demand-ability fit (i.e., environment demands vs. individual abilities, D-A fit; e.g., French, Caplan, & Harrison, 1982) may help explain thedifferential effectiveness of PRA applied to studies that examined different type of assumed outcomes. Although two out of the 30studies in our meta-analysis actually examined S-V fit and D-A fit at the same time while predicting various outcomes (Edwards,1996; Livingstone et al., 1997), most of the studies took the perspective of S-V fit which should contribute more to the social andpsychological environment where the technical core of the organization operates (Organ, 1997) than D-A fit. In this sense,employees' job attitudes and contextual performancemay bemore reactive to the interactions between individuals and their workenvironment at value level (i.e., supply-value fit), while their task performance shall be more responsive to P-E interactions onwork demands vs. individual abilities. These speculations should be tested in future studies and our results need to be viewedcautiously due to the relatively small number of studies looking at contextual (six) or task (four) performance.

4.4. Implications and limitations

In all, ourmeta-analysis is one of the first attempts to integrate the literature of applying PRA in the field of P-E fit quantitatively.A unique type of effect size (R2 change) was chosen to best reflect the incremental validity of PRA over and above linear regressionin explaining outcome variables. With a unique algorithm, we managed to answer the three key research questions proposed andprovided some insight into using PRA appropriately and effectively for future researchers who are interested in conductingresearch on P-E fit, or its sub-types.

Despite the merits of our meta-analysis, a few limitations deserve mention here. First, not all the studies of P-E fit using PRAwere included given the limits of the availability of effect size information we requested from researchers. One must, in view ofthis, evaluate the results of ourmeta-analysis with caution as a conclusive review of the literature of applying PRA in the area of P-Efit. Second, all the previous studies which applied PRA utilized a non-experimental design, which precludes us from making anycausal conclusion about the influence of P-E fit on various work outcomes based upon the current meta-analysis (e.g., Shadish,Cook, & Campbell, 2002; Stone-Romero & Rosopa, 2008). In addition, the inter-dependent regressionmodels from the same samplewere combined, which reduced the informationwe could use. However, given the uniqueness of ourmeta-analysis, we believe thatutilizing one study-level effect size from each sample should contribute to less biased parameter estimates by avoiding thedependence among effect sizes (Lipsey & Wilson, 2001) and reducing the potential occurrence of Type I errors from multipleregression analyses with each sample. Finally, the advantages of PRAmay not be fully reflected by the R2 change because the three-dimensional interpretation of the relation among P, E and assumed outcomes offered by PRA provides a more complete picture ofoutcomes with the supplement of response surface methodology (Box & Draper, 1987; Edwards & Parry, 1993), as opposed to usingjust linear regression. Rather, we argue that R2 change is a good effect size index in this particular case, because it containssufficient quantitative information on PRA's advantages over linear regression. Therefore, we believe that the results of our meta-analysis provide useful insights for the effectiveness of applying PRA in the research on P-E fit.

We may also consider other potential moderators in future meta-analyses like different content dimensions (e.g.,polychronicity at work, job complexity or compensation) of fit, or type of industry (e.g., sales, high-technology, or manufacturing),different occupations (e.g., customer service representative, researcher or engineer), or whether PRA results are cross-validated ornot, when sufficient number of studies available in the literature. Specifically, given differences in the relative importance ofdifferent content dimensions of fit for employees, we suspect that P-E interactions explain their attitudes and behaviors betterfor some dimensions than others (e.g., Edwards, 1996). To put this in a different way, for some content dimensions, it is possiblethat “P+E” does not explain sufficient variance in assumed outcome variables but the non-linear terms of PRA add substantially tothe prediction of such outcomes. Besides, people in different industries or with different occupations may value P-E fit to differentdegrees such that people from a certain industry (e.g., high-technology) or in a certain occupation (e.g., researcher) strive more toreach better P-E fit at work and react more strongly to misfit than their counterparts in other industries or occupations. Finally,when enough studies applying PRA and cross-validating the regression are done in the future, it will be interesting to examinewhether the effectiveness of PRA is different for the studies using cross-validation vs. those without. With such endeavors, we willbe able to gain a better understanding of the rigor of PRA.

Given the elegance of the approach, we believe there are a number of areas in human resource management that could makeuse of PRA in research, and applications that may be derived from the research, when PRA provides solid evidence for theadvantage of fit and the nature of fit (e.g., complementary or supplementary) that works best. The foundational research can focuson different types of relevant and important management outcomes, including employee attitudes, behaviors and performance.Some of these areas are mentioned above. For instance, many organizations use a career tracking system for developing futureemployees in various functions; PRA research has the potential for suggesting the best tracks for employees based on matchingvarious individual and organizational factors (e.g., values). In addition, research on recruiting sources could use PRA whenevaluating if there are different on-boarding strategies that work best for employees from different recruitment sources. Also,

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diversity management could be the focus of PRA research; for example research could address whether employees from differentethnic backgrounds prefer or benefit from different organizational practices. Yet another potential application could be toinvestigate the consequences of differences or similarities in negotiation styles. Clearly, PRA offers promise but must rely on goodmeasurement, favorable research conditions, and replication of results to inform evidence-based management practices.

Acknowledgement

We thank Dr. Michael T. Brannick's for his help on the method used for this manuscript, and thank Dr. Eugene F. Stone-Romerofor his assistance in refining our paper. We also thank Charleen Maher for her help with the literature search.

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