Applications of Item Response Theory to Measurement Issues in Leadership Research

7/29/2019 Applications of Item Response Theory to Measurement Issues in Leadership Research

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Applications of item response theory to measurement issues in leadership research

Charles A. Scherbauma, , , Scott Finlinsonb, Kira Bardena and Kevin Tamaninib

aDepartment of Psychology, Baruch College, City University of New York, Box B 8-215, One

Bernard Baruch Way, New York, NY 10010, USA bOhio University, USA, FinnERGY, USA

Available online 30 June 2006.

Abstract

The measurement of a variety of leadership constructs has been a persistent source of debate and

critique for many areas of leadership research. As such, leadership researchers have devoted

substantial efforts to demonstrating the psychometric quality of their measures. Yet, the techniques

used in these efforts have not kept pace with the advances in psychometric theory and methods.

This is regrettable given that modern psychometric techniques, such as item response theory,

provide additional insights over and above those gained from classical psychometric techniques.This paper presents an introduction to item response theory and demonstrates the application of

both cumulative and unfolding IRT models to measurement issues in leadership research using

leadermember exchange as an example.

Keywords: Leadership measurement; Item response theory; Leadermember exchange; Unfolding

IRT models; Psychometric techniques

Article Outline

1. Introduction2. Measurement issues in leadership research

2.1. Leadermember exchange

3. Item response theory

3.1. Cumulative IRT models

3.1.1. Graded response models

3.2. Unfolding IRT models

3.3. Assumptions of item response theory

3.4. Advantages of item response theory over classical methods

3.5. Limitations of item response theory

3.6. When should IRT be used over classical methods?

4. Summary5. Method

5.1. Participants

5.2. Measures

5.2.1. Multidimensional leadermember exchange scale

5.2.2. Demographic characteristics

5.3. Analyses

5.3.1. Classical psychometric analyses

5.3.2. Modified parallel analysis

5.3.3. Parameter estimation, item and test information, and model fit

6. Results

6.1. Classical psychometric analyses6.2. Modified parallel analysis

6.3. Parameter estimates
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6.4. Tests of model fit

6.5. Item and test information functions

6.6. Summary of results

7. Conclusion

7.1. Additional directions for the use of item response theory in leadership research

7.2. Summary

AcknowledgementsReferences

1. Introduction

Leadership research is often concerned with the measurement of psychological, attitudinal, and

cognitive constructs from followers about their leaders and vice versa (Clark and Clark, 1990 and

Yukl, 1989). As the work of Lord and others (e.g., Foti and Lord, 1987, Lord et al., 1984,Osborn et

al., 2002 and Phillips and Lord, 1986) has demonstrated, measurement of these constructs can be a

very complicated and difficult issue for leadership research. Correspondingly, the importance of

understanding the psychometric properties of our leadership measures has been recognized for some

time (e.g., Korman, 1974, Schriesheim and Kerr, 1974,Schriesheim and Kerr, 1977 andSchriesheim et al., 1993). Recently, there has been a marked increase of interest in more detailed

treatments of the psychometric properties of the measures used in leadership research (e.g.,

Antonakis et al., 2003,Liden and Maslyn, 1998 and Tejeda et al., 2001). Moreover, there are

several excellent demonstrations of the consequences that insufficient attention to psychometric

properties can have on the nature of the conclusions drawn from leadership research (e.g., Keller

and Dansereau, 2001, Podsakoff et al., 2003 and Schriesheim et al., 1993). Despite the importance

of measurement for leadership research, the use of psychometric techniques has not kept pace with

the advances in psychometric theory and methods.

The last forty years have been witness to major developments in techniques for understanding the

psychometric properties of cognitive, attitudinal, and psychological measures. The most notable

development is item response theory (IRT). IRT is a family of techniques for understanding the

psychometric properties of measures and relationships between properties of the measures and the

individuals completing those measures. These techniques have been used to advance our

understanding in a variety of domains of organizational research ranging from multisource

performance ratings (e.g., Facteau & Craig, 2001), to dishonest responding on personality

inventories (e.g.,Zickar & Robie, 1999), to cross-cultural differences in employee attitudes (e.g.,

Ryan, Horvath, Ployhart, Schmitt, & Slade, 2000).

Unfortunately, research in the area of leadership has not yet embraced these techniques (see Craig

& Gustafson, 1998 for an exception). This is regrettable as modern psychometric techniquesprovide additional insights over and above those gained from classical psychometric techniques

(Embretson and Reise, 2000 and Reise and Henson, 2003) and have much to offer to leadership

research. As noted above, many of the constructs of interest in leadership research are assessed

using self-report or other-report measures and the conceptualization of these constructs is becoming

more complex (e.g., Marion and Uhl-Bien, 2001and Osborn et al., 2002). As such, gaining a better

understanding of the measures used to support leadership theories and constructs is a prudent course

for leadership research to take (Schriesheim et al., 1993).

The purpose of this paper is to present an introduction to item response theory and demonstrate the

application of two different classes of IRT models (i.e., cumulative and unfolding models) to

measurement issues in leadership research using the Multidimensional LeaderMember Exchangescale (LMXMDM; Liden & Maslyn, 1998) as an example. We focus this demonstration on the

aspects of IRT that allow for a deeper understanding of the psychometric properties of leadership
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measures and the application of the recently developed unfolding IRT models. In the subsequent

sections, we briefly review issues surrounding measurement in leadership research, present the

basic principles of IRT, describe the cumulative and unfolding IRT models, and the methodology

employed in our example.

2. Measurement issues in leadership research

The research methodology appropriate for studying leadership has been a continual source of debate

(Alvesson, 1996,Clark and Clark, 1990, Hunt, 1999, Yukl, 1989 andYukl and Van Fleet, 1992).

Although there are a variety of ways to measure leadership constructs, the majority of leadership

research has relied on some form of survey methodology. In fact, most major leadership theories

(e.g., Fiedler's contingency theory) have an associated measure (e.g., least-preferred co-worker

scale) that is used to test the propositions of the theory or describe individuals in terms of some

leadership construct.

As leadership theories and research have proliferated, the catalog of leadership measures available

for research and practice has grown at leaps and bounds (e.g., Clark and Clark, 1990 and

Schriesheim et al., 1993). Currently, there is an almost dizzying set of options available. Typically,the choice of a particular measure is based on the particular operationalization of leadership and the

psychometric properties of the measure. Fortunately, serious attention has been paid to the

psychometric properties of some of these measures (e.g., Schriesheim & Kerr, 1974). Therefore, a

substantial body of evidence concerning the reliability and construct validity has accumulated for

several of the measures.

Nevertheless, some of the most prominent leadership measures have suffered from debates

concerning the nature of the construct measured and the quality of the psychometric evidence for

the measurement of the construct. For example, two recent studies (e.g., Antonakis et al., 2003 and

Tejeda et al., 2001) have presented conflicting evidence about the factor structure and psychometric

quality of the Multifactor Leadership Questionnaire (Bass & Avolio, 1993). These types of

conflicting results cast a shadow over the quality of the psychometric evidence for leadership

measures and the interpretation of the findings from studies using these measures (Schriesheim et

al., 1993). Most recently, debates concerning these measurement issues have been highly visible in

the literature on leadermember exchange (e.g., Schriesheim, Castro, & Coligser, 1999).

2.1. Leadermember exchange

Leadermember exchange has become one of the most heavily studied topics in the domain of

leadership (Gerstner & Day, 1997). Beginning with the early vertical-dyadic linkage model, the

concept of leadermember exchange has evolved into a variety of approaches for understandingleader member exchanges (LMX; Graen and Uhl-Bien, 1995,Liden et al., 1997, Schriesheim et al.,

1999 and Yukl, 1989). As it is currently operationalized, LMX describes the unique relationships a

supervisor may have with each of his or her subordinates (Liden et al., 1997). According to LMX,

supervisors form differentiated relationships with subordinates such that there are groups of high

and low LMX subordinates. As a result, there is variability in the frequency and quality of

interactions for those in the different LMX groups. These differentiated relationships predict a

number of important outcomes at multiple levels of analysis (Gerstner & Day, 1997).

Though frequently studied, LMX has also become one of the most convoluted areas of leadership

research (Schriesheim et al., 1999). As a result, there is disagreement about what LMX is, the

dimensionality of the construct, the appropriate level of analysis, and how it should be measured(Gerstner and Day, 1997,Liden and Maslyn, 1998, Liden et al., 1997 and Schriesheim et al., 1999).

In particular, the psychometric properties and use of LMX measures has been a particular area of
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contention (Barge and Schlueter, 1991, Keller and Dansereau, 2001,Liden and Maslyn, 1998 and

Yukl, 1994).

Currently, there are over fifteen different measures of LMX and several variations of some of these

measures (see Schriesheim et al., 1999for a review of the measures).Dienesch & Liden (1986) and

others (e.g.,Schriesheim et al., 1999 andVecchio and Gobdel, 1984) have argued that solid

psychometric evidence is lacking for most of these measures. Further, a meta-analysis byGerstner& Day (1997) found some support for the position that LMX measures are moderators of the

relationship between leadermember exchange and organizationally relevant outcome variables.

Thus, the nature of the findings may, in part, depend on the LMX measure that is used in a given

study.

Although there are several measures that have been offered as the gold standard (e.g., LMX-7,

Graen & Uhl-Bien, 1995), there is little psychometric evidence supporting the gold standard status

of any LMX measure (Schriesheim et al., 1999). The evidence that has been presented is difficult to

interpret because there have been so many modifications to many of these LMX measures. Even

slight modifications can have a large impact on the psychometric properties of a measure (e.g.,

Keller and Dansereau, 2001 and Schriesheim et al., 1993). The result is that there are many differentLMX measures, but there is little rigorous psychometric evidence for most of the measures.

Common to all of the research on the measurement of LMX is that the psychometric properties have

been established using classical psychometric techniques. Without question, this research has

become increasingly sophisticated as it has moved from simple reliability indices to complex

covariance structure models. Nevertheless, no research to date has examined the psychometric

properties of measures of leader member exchange using modern psychometric techniques such as

those from item response theory. This is unfortunate given that modern techniques like item

response theory (IRT) are well suited to address many of the issues that have been raised

concerning the measurement of LMX and other leadership measures. The purpose of this paper is to

provide an introduction to cumulative and unfolding IRT models and a demonstration of how these

IRT models can be used to examine measurement issues in leadership research. In the subsequent

sections, we describe basic concepts in item response theory, the cumulative and unfolding IRT

models, and the applications of these models to measurement issues in leadership research.

3. Item response theory

Item response theory (IRT) is a model-based (i.e., mathematical) approach to understanding the

non-linear relationships between individual characteristics (e.g., ability, traits), item characteristics

(e.g., difficulty), and individuals' response patterns (Drasgow & Hulin, 1990). Thus, IRT is

concerned with estimating parameters of the items on a measure and parameters of the individualswho complete those measures. For example, with an LMX measure, an IRT analysis could estimate

the respondent's level of exchange quality (i.e., a person parameter) and how well the items on the

measure discriminate between individuals with different levels of exchange quality (i.e., an item

parameter).

Classical psychometric procedures rely on total scores and correlations as a basis for the person and

item parameters. IRT, on the other hand, estimates latent parameters for the persons (i.e., the

characteristic underlying the total scores) and items using the responses gathered from the sample of

data. Moreover, the estimated person and item parameters in IRT are invariant. That is, they are

independent of one another. The item parameters do not depend on the distribution of the

characteristic in the sample and the person parameters do not depend on particular items on ameasure (Hambleton, Swaminathan, & Rogers, 1991). Therefore, the item parameters are not

needed to interpret the person parameters and vice versa. With classical psychometric techniques,
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this is not the case, as the person parameters or item parameters cannot be understood out of the

context of each other. Moreover, with IRT, the items and persons are on the same metric (i.e., z-

scores). Therefore, the level of a characteristic an individual possesses can be compared to the level

of the characteristic required by the item. With classical methods, individuals can only be compared

to other individuals or an external standard (e.g., a cut score).

IRT is best classified as a family of different models. Although there are many differences betweenthe available models (e.g., use of binary vs. polytomous data), one major distinction between IRT

models concerns the assumption about the relationship between the selection of a response options

and the level of the latent trait. For cumulative IRT models the assumption is that there is an

increased probability of selecting the correct or higher-ordered response options as the level of the

latent trait increases. That is, there is a monotonic relationship between the response choice and the

level of the latent trait. Consequently, the individuals with the highest levels of the latent trait will

have the highest scores on the items. Another possible assumption is that the relationship is non-

monotonic. More specifically, there is an ideal point for each individual on the continuum of a

latent trait and the response option nearest the ideal point will be selected. Consequently, the

individuals with a level of the latent trait that is closest to the level expressed in the item will have

the highest score on the item. This notion is based on Coombs, 1950 and Coombs, 1964 andThurstone, 1928 and Thurstone, 1931 research on ideal point response processes. This class of IRT

models is referred to as unfolding models (Roberts, 1995 andRoberts and Laughlin, 1996). These

models are relatively new and not widely known outside of the measurement literature. However,

they have great potential for application in leadership and organizational research as ideal point

processes may underlie the responses to many organizationally relevant phenomena (Drasgow,

2003) and attitudinal variables in general (Roberts, Laughlin, & Wedell, 1999).

In the subsequent sections, a cumulative IRT model that is commonly used with graded response

data (e.g., Likert-type response scales) is briefly described. Additionally, the unfolding IRT models

are introduced and described in some detail. Following the descriptions of the IRT models, an

example of a cumulative and unfolding IRT model is presented using data fromLiden & Maslyn's

(1998) Multidimensional LeaderMember Exchange scale. The results from the IRT models are

compared with each other and to the results from a classical item analysis.

3.1. Cumulative IRT models

As noted above, cumulative IRT models are built on the notion that the relationship between

individuals' latent characteristics (i.e., intelligence, exchange quality) and individuals' response

selection is a monotonic function. This perspective is often referred to as dominance response

processes and is rooted in the work ofLikert (1932) and Guttman (1950). Many of the well-known

IRT models (e.g., Rasch models, logistic models, Samejima's (1969) graded response model,Master's (1982) partial credit model) are cumulative models. In this paper,Samejima's (1969)

graded response model is discussed. This model is one of the most commonly used cumulative IRT

models in organizational research. As this model may be familiar to many readers, the description

provided here is brief and introductory. The reader is referred to Embretson & Reise (2000)orvan

der Linden & Hambleton (1997) for more detailed treatments of the cumulative models.

3.1.1. Graded response models

In most leadership, attitudinal, and personality research, the measures utilize response options that

are ordered (e.g., Likert-type response options) and the data are used to make conclusions

concerning the level of the construct that is assessed by the measure. In these cases, graded responsemodels can be used. In these models, the IRT analysis examines the relationships between item or

option parameters, person parameters, and the selection of a particular option. For cumulative
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