Measurement Properties of Constraints to Sport Participation: A Psychometric Examination with Adolescents

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Measurement Properties of Constraints to Sport Participation: APsychometric Examination with AdolescentsJonathan M. Caspera; Jason N. Bocarroa; Michael A. Kantersa; Myron F. Floyda

a Parks, Recreation and Tourism Management, North Carolina State University, Raleigh, NC, USA

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To cite this Article Casper, Jonathan M. , Bocarro, Jason N. , Kanters, Michael A. and Floyd, Myron F.(2011) 'MeasurementProperties of Constraints to Sport Participation: A Psychometric Examination with Adolescents', Leisure Sciences, 33: 2,127 — 146To link to this Article: DOI: 10.1080/01490400.2011.550221URL: http://dx.doi.org/10.1080/01490400.2011.550221

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Leisure Sciences, 33: 127–146, 2011Copyright C© Taylor & Francis Group, LLCISSN: 0149-0400 print / 1521-0588 onlineDOI: 10.1080/01490400.2011.550221

Measurement Properties of Constraints to SportParticipation: A Psychometric Examination

with Adolescents

JONATHAN M. CASPERJASON N. BOCARROMICHAEL A. KANTERSMYRON F. FLOYD

Parks, Recreation and Tourism ManagementNorth Carolina State UniversityRaleigh, NC, USA

Constraint are a major focus of theoretical and empirical study in leisure research.However, analyses of psychometric properties of constraints measures are rare. Thisstudy assessed the factor structure and invariance of a leisure constraints measureapplied to sport participation among middle school adolescents (ages 11 to 15 yearsold) using panel data over two time periods nine months apart (N = 2,029). We comparedthe validity of three baseline models: a theoretical 3-factor model, a 7-factor model,and a second-order factor model. The 7-factor model exhibited a more appropriatemeasurement model based on fit indices and statistical comparisons. Using the 7-factor model, construct validity and invariance of the model over time (Time 1 andTime 2) was examined by gender, grade level, race/ethnicity, and socioeconomic status.The model was found to be invariant at the factor loading and intercept levels, whilethere was some evidence of non-invariance at further constrained levels. In general,the 7-factor model appeared to be psychometrically stable and applicable over a rangeof demographic subgroups, lending evidence to its use as a measure in leisure orsport participation constraint studies that involve socio-demographic comparisons. Thefindings suggest that while the theoretical structure may be effective in simplifyingconstraint categories, a more detailed specification using subfactors of the dimensionsis better for measurement.

Keywords adolescents, barriers, constraints, invariance, measurement, middle school,sport

Understanding constraints to leisure has become a major focus of theoretical and empir-ical study over the last two decades. This intense focus has been attributed in part to itscapacity to generate hypotheses and new theory within constraints research and in othersubfields of leisure studies (Shores, Scott, & Floyd, 2007). Indeed, conceptual developmentwithin the constraints literature has been markedly robust. The literature has evolved toaccount for prohibitive factors that affect the formation of leisure preferences as well as

Received 4 March 2010; accepted 30 November 2010.Address correspondence to Jonathan M. Casper, Box 8004, 3033B Biltmore Hall, Parks, Recreation

and Tourism Management, North Carolina State University, Raleigh, NC 27695-8004. E-mail: [email protected]

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128 J. M. Casper et al.

actual participation, pathways, and processes through which constraints operate; sequenc-ing of constraint processes; and more recently, patterns in negotiation processes (Jackson,2005). These developments rest on a substantial base of empirical studies of a variety ofparticipant groups, environments, and program settings and include quantitative and quali-tative analyses (Jackson, 2005). Despite increased theoretical sophistication and empiricalstudies, investigations that have focused on the construct validity of constraint conceptsand the extent that findings can be generalized to different social groups are uncommon.Recently, researchers have called for greater consideration of the potential systematic vari-ations in constraints and the process of negotiating constraints across population subgroups(Crawford & Jackson, 2005; Shores et al., 2007).

Advances in quantitative research on leisure constraints hinge on the quality ofmeasures developed to represent underlying constructs involved in constraint processes(Mannell & Iwasaki, 2005). The purpose of the current study was to examine the psycho-metric properties of a constraints survey instrument applied to sport participation amongadolescents (ages 11–15). Utilizing individual-level panel data, we examined model speci-fication/structure by assessing three baseline models (3-factor, 7-factor, and second-order).We then investigated factorial validity, reliability, and invariance of the most appropriatebaseline model by gender, race/ethnicity, socioeconomic status (SES), and longitudinally.

Background

Leisure Constraints Theory and Models

Constraints theory recognizes three types of constraints (intrapersonal, interpersonal, andstructural) that affect leisure preferences and participation (Crawford & Godbey, 1987;Crawford, Jackson, & Godbey, 1991). Intrapersonal constraints refer to individual psycho-logical states and attributes that inhibit formation of leisure preferences and leisure par-ticipation. This category of constraints is usually measured by assessing perceived skills,abilities, and beliefs or attitudes about the appropriateness of activities and the availabilityof opportunities. Interpersonal constraints are defined as factors associated with relation-ships with individuals or groups such as the inability to find partners. Structural constraintsare barriers imposed by social institutions, organizations, or belief systems external to anindividual (Raymore, 2002) that affect the formation of leisure preferences and intervenebetween preference and participation. This category of constraints usually includes factorsassociated with the availability of resources required to participate such as money, time,problems with facilities, and social/geographical isolation.

Constraint measures have been employed in diverse contexts, including recreationalsports (Alexandris & Carroll, 1997a, 1997b; Alexandris, Kouthouis, Funk, & Chatzigianni,2008), travel and tourism (Funk, Alexandris, & Ping, 2009; Nyaupane, 2005; Pennington-Gray & Kerstetter, 2002), initiating new or continued participation in leisure activities(Shinew, Floyd, & Parry, 2004; Walker, Jackson, & Deng, 2008), outdoor recreation (White,2008; Wright, Rodgers Drogin, & Backman, 2001), and urban and state park use (Mowen,Payne, & Scott, 2005; Scott & Munson, 1994; Wilhelm-Stanis, Schneider, & Anderson,2009). While findings from these studies have increased the understanding of similaritiesand differences between and within populations or activity groups, instrumentation andmeasurement vary. Most constraint measures and scale items used in previous researchoriginate from seminal work by Crawford and Godbey (1987) and Crawford et al. (1991).Some researchers have based their measurement on the theoretical 3-factor model reflectingCrawford and Godbey’s reconceptualization (intrapersonal, interpersonal, and structural),while others studies have further divided the theoretical factors into multiple dimensions


Measurement Properties of Constraints 129

that hierarchically link to the three theoretical factors. Recent studies implementing the the-oretical 3-factor model (e.g., White, 2008) have adopted items from Hubbard and Mannell(2001) and Raymore et al. (1993). Other constraint studies (e.g., Alexandris, Tsorbatzoudis,& Grouios, 2002; Tsai & Coleman, 2009), have selected items and created factors basedon relevance to specific leisure activities and/or population (e.g., park visitors, exercisingadults, recreational sport), personal knowledge of a domain, or qualitative interviews withindividuals (Mannell & Iwasaki, 2005). While the selected (or created) factors may theo-retically relate to the fundamental three dimensions, measurement has been conducted ata factor (or variable) level so several factors may represent first order factors of a singlesecond order dimension (e.g., interest and knowledge represent the theoretical intrapersonaldimension). Typically, these first order factors have been formed based on meaning (facevalidity) or exploratory factor analysis, where items loaded on unique factors.

Past research reveals measurement inconsistencies associated with measurement mod-els. For example, Wilhelm-Stanis, Schneider, and Anderson (2009) used the theoretical3-factor structure where 31 items represented the three factors. Alexandris, Kouthouris,and Grouios (2002) used a 7-factor structure (Alexandris & Carroll, 1997a) where itemswere categorized into seven factors (individual/psychological, lack of knowledge, lackof interest, lack of partners, facilities/services, accessibility/financial, and time) based onexploratory factor analysis. In both studies, the constraint measure was used in conjunc-tion with a negotiation measure. However, Wilhelm-Stanis et al. found that the internalreliability for structural constraints was low (α = .58) but concluded that the factor wasacceptable because previous studies, such as Hubbard and Mannell (2001), also reportedlow reliabilities. Conversely, the number of factors extracted and factor structures has beeninconsistent. Furthermore, confirmatory analysis of the three theoretical dimensions hasbeen mixed in this literature. Raymore et al. (1993) found evidence to support the the-oretical 3-factor subscales, while other studies attempting to replicate these results didnot find evidence supporting a 3-factor solution (Hawkins, Peng, Hsieh, & Eklund, 1999;Hubbard & Mannell, 2001). A possible explanation for these inconsistent findings is thatitems representing a particular theoretical factor can be dissimilar. For example, within thestructural constraints factor, an item relating to “not having enough time” is fundamentallydifferent in terms of content from an item related to “access to facilities.” Therefore, it ap-pears that items relating to the three dimensions may overlap (i.e., cross-load) throughoutthe three factors (Mannell & Iwasaki, 2005), which results in some of the aforementionedmeasurement inconsistencies, and hence model misspecification.

Finally, factors (or subscales) are typically calculated as part of a factor total (or mean).These totals (or means) are then used in further analysis to examine relationships with othermeasures such as negotiation or participation. Results from such analyses are influenced bythe factor structure of a constraints measure. Without unifying factor structure, comparisonof results or validity of findings is limited. Thus, inconsistencies in factor structures andmodel specification with constraints measures should be of concern.

Factorial Validity and Invariance

In addition to inconsistent instrumentation and model specification, reporting of psychome-tric results in leisure constraints research has been limited (e.g., an exploratory analysis orconfirmatory factor analysis). While confirmatory factor analysis has been the norm in morerecent studies (e.g., Nyaupane, 2005; Pennington-Gray & Kerstetter, 2002; Tsai & Colman,2009), invariance has not been reported. Measurement invariance refers to the degree towhich measurements conducted under different conditions exhibit similar psychometric



properties (Byrne, 2008). Establishing multigroup or longitudinal factorial invariance us-ing confirmatory factor analysis is essential to determining whether differences in scoresindicate true differences or effects rather than a change in the factor structure or loadings.Recently, research involving tests of measurement invariance has increased due in partto growing awareness of the importance of comparing and assessing measures (Meade &Lautenschlager, 2004). Examples of different conditions associated with invariance includemeasurements conducted over time (e.g., Chan, 1998; Chan & Schmitt, 2000) and acrossdifferent cultures (Riordan & Vandenberg, 1994), gender (Marsh, 1987), and age groups(Marsh & Hocevar, 1985).

Invariance analysis with constraints measures is particularly important due to the sub-stantial amount of research implementing socio-demographic comparisons. For example,several studies demonstrate that constraints vary by race and ethnicity (Arnold & Shinew,1998; Mowen et al., 2005; Shinew, Floyd, & Parry, 2004), socioeconomic status (Scott &Munson, 1994), and gender (Shores et al., 2007). Regarding age, the prevailing finding isthat experience or perception of constraints increases with age (Scott & Jackson, 1996;Shores et al., 2007; Wang, Norman, & McGuire, 2005). Three studies have examined con-straints longitudinally (Jackson & Witt, 1994; Mowen et al., 2005; Wright et al., 2001).The measures employed in these studies emphasized structural constraints rather than in-terpersonal and intrapersonal constraints, and none used panel data. Collectively, these andsimilar studies are important for documenting how constraints can differ between socialgroups or over time. However, without established invariance, differences in perceived con-straints may be more attributable to measurement (e.g., differences in item interpretation)rather than true differences between groups.

Rationale and Purpose

Despite the relatively large amount of research devoted to leisure constraints, four mea-surement issues remain unaddressed. First, measurement has been inconsistent related tofactor structure and no study has assessed the tenability of different factor structures withthe same constraint instrument. Second, psychometric equivalence of constraint measuresacross population subgroups and participant groups is rarely tested. Third, the use of paneldata to test for invariance in constraints has not been utilized previously. Finally, there arelimited data on the appropriateness of constraints research among adolescents (Jackson& Rucks, 1995; Raymore, Godbey, & Crawford, 1994) despite the importance of adoles-cence as a critical developmental phase in the formation of leisure preferences (Caldwell &Baldwin, 2005). Given these issues, this study critically examined the psychometric prop-erties of a commonly used constraint scale using individual-level panel data of a relativelylarge and diverse sample of adolescent youth.

The specific objectives of this study focused on perceived constraints to sport partic-ipation were twofold. First, we compared the fit of three alternative factor structures ofa constraint measure. These were a theoretical 3-factor structure, a 7-factor model, anda second-order model that tests the hierarchal structure of the 3-factor and the 7-factormodels. The second objective was to assess factorial validity and invariance longitudinallyand based on comparisons of socio-demographic subgroups of adolescents.

Methods

Participants and Procedure

This study was part of a larger study focusing on middle-school sport participation. Datacollection procedures were reviewed and approved by both the Institutional Review Boardat the researchers’ university and the local public school district’s Evaluation and Research



Department. Data were obtained by an online self-administered survey conducted at fourpublic middle schools (grades 6–8) in the southeastern United States. The questionnairewas reviewed by school administrators and a pilot test was conducted with local middleschool children not part of the study. Each school provided computers where the surveyWeb site was preloaded. The survey was administered at two time periods approximatelynine months apart. Data were collected in early September 2008 about two weeks into thetraditional school year (Time 1, N = 2,587). Follow-up data collection was conducted inMay 2009 about four weeks prior to the conclusion of the school year (Time 2, N = 2,582).For the purposes of this study, only respondents who completed the survey in Time 1 andTime 2 and whose identity could be matched based on an identifying code were includedin the analysis (n = 2,029).

Measures

Since the study focused on sport participation, constraint items were derived from previousconstraint research on recreational sport (Alexandris & Carroll, 1997a, 1997b; Alexandris& Stodolska, 2004). Item wording was modified for youth sports (see Table 3). Thismeasure was chosen because the items represent each of the three theoretical constraintdimensions (intrapersonal, interpersonal, and structural constraints) while also representingseven subfactors that have been found to be unique based on factor analysis and face va-lidity. Specifically, the 25-item scale represented the following seven factors: accessibility,facility cleanliness, interest, knowledge, psychological, social support/partners, and time.Intrapersonal constraints were related to psychological, knowledge, and interest factors;interpersonal constraints were represented by the social support/partners factor; structuralconstraints were represented by accessibility, facilities, and time factors. Respondents wereasked how much each of the constraint items prevented them from playing more sports.Each item was measured on a 5-point Likert-type scale indicating level of agreementranging from 1 (not at all) to 5 (all the time). Socio-demographic categories were basedon responses for sex, race/ethnicity, and parent’s SES (receiving a free or reduced pricelunch). Native American/Alaskan, Asian, and those who chose “other” were not includedin the race/ethnicity analysis due to low frequencies (<3%). Characteristics of the samplebased on the fall data collection period (Time 1) which was at the beginning of the schoolyear are presented in Table 1.

Data Analysis

Baseline model. Initially, univariate normality of each constraint item was assessedby examining skewness and kurtosis and examining critical values (skewness less than+/− 2.0 and kurtosis less than +/− 7.0) while multivariate normality was assessed basedon relative multivariate kurtosis (critical values less than 2.0) (Tabachnick & Fiddell, 2001).Measurement models were tested using confirmatory factor analysis (CFA) with full-information maximum likelihood (FIML) in AMOS 16.0. FIML was used for estimationbecause missing responses are common in school-based, longitudinal research with largesamples (Motl et al., 2000), and it yields accurate fit indices and parameter estimateswith up to 25% missing data (Enders & Bandalos, 2001). The overall fit of models wasassessed using the following fit indices: chi-square/degree of freedom ratio, Comparative FitIndex (CFI), Tucker Lewis Index (TLI), and Root Mean Squares Error of Approximation(RMSEA). A chi-square/degrees of freedom ratio of less than 2.0 indicated acceptableoverall fit (Marsh, Balla, & McDonald, 1988). CFI and TLI values .90 and above indicated



TABLE 1 Characteristics of the Study Respondents (Time 1 Data Collection)

Socio-Demographic Category N %

GenderFemale 982 50.9Male 1019 48.4

Grade6th 658 32.67th 636 31.58th 727 36

RaceAfrican American 624 31.4Hispanic 178 9.0White 1043 52.5Other 141 7.1

Family Income (receives free or reduced lunch)Yes 575 28.7No 1427 71.3

acceptable fit, and RMSEA values of .05 or less indicated acceptable fit (Hu & Bentler,1999).

To address the first research objective, three measurement models were comparedin order to identify the most appropriate baseline model for invariance tests (Figure 1).We examined a model that grouped the items into 7-factors (e.g., Alexandris & Carroll,1997a, 1997b) based on face validity of the items (e.g., “I don’t have enough time” loadedto a Time factor). The 3-factor model had items relating to each theoretical dimensionloaded to the appropriate factor (e.g., Son, Mowen, & Kerstetter, 2008; White, 2008;Wilhelm-Stanis, Schneider, & Russell, 2009). For this model, the covariance’s of the threefactors representing structural constraints and the three factors representing interpersonalconstraints were fixed so that covariance’s between intrapersonal, interpersonal (which wasrepresented by one factor), and structural factors could be freely estimated. This “nested”approach yields identical fit indices as a specification where the items representing eachfactors are directly loaded to the three factors and allows for a likelihood ratio test of the3- and 7-factor model specification. The second-order model is a specification where thefirst order factors (equivalent to the 7-factor model) are explained by a higher second-orderstructure (the theoretical 3-factor). With this model the second-order factors (intrapersonal,intrapersonal, and structural) freely correlate and load to the first-order factors.

FIGURE 1 Construct-level depiction of the three baseline models tested.



Comparisons of model specification were made based on the model fit indexes. Statis-tical comparison of the 3- and 7-factor models used a likelihood ratio test based on changesin chi-square. The difference in chi-square between the 7- and “nested” 3-factor models(and change in degrees of freedom) were then used to determine if there was a significant(p < .05) change in fit between models. If the change was significant, the model with thebest fit indices was considered the most appropriate measurement model. If there was anonsignificant change, then the more parsimonious model (the 3-factor model in this study)was considered the more appropriate model. Analysis of the second-order model with the3- and 7- factor models was compared descriptively based on fit indexes. If the fit wassimilar, the more parsimonious model was designated the more appropriate measurementmodel. Once the most appropriate model was determined, a CFA was conducted to examinestructural aspects of factor validity. We reported standardized factor loadings and factorreliability for both Time 1 and Time 2. Thresholds for factor loadings were loading scoresabove .40 (Raubenheimer, 2004) and Cronbach alpha reliability scores above .70 (Nunnally& Bernstein, 1994).

Invariance tests. Procedures for invariance testing followed previous studies of psy-chometric assessment and invariance (Marsh, 1994; Motl et al., 2000; Nigg, Lippke, &Maddock, 2009; Paxton et al., 2008). Initially, the measurement found to be most accept-able in the “baseline model analysis” was tested, via CFA, individually for each group (e.g.,Whites, Males). After testing the overall model with each subgroup, we placed constraintsin a sequence of models: Model 1) the model supported from the “baseline model” analyses;Model 2) testing equal factor loadings across the samples; Model 3) model 2 constraintsplus equal measurement intercepts; Model 4) model 3 constraints plus structural varianceand co-variances; and Model 5) model 4 constraints plus measurement residuals (error).We then compared the models based on χ2 differences in relation to changes in degrees offreedom (df ) of the unconstrained model (Model 1). This indicated if there were significant(p < .05) differences between the models. Since CFA tests for invariance have been foundto be highly sensitive to sample size (Meade, Johnson, & Braddy, 2008) we observed theTLI where changes less than or equal to 0.01 suggest that invariance of an instrumentshould not be rejected (Byrne, 2008). Therefore, if the χ2 differences test is significant butthe fit indices change is less than .01, there is evidence for the equivalence/invariance ofthe model structure or parameters between groups. Interpretation of invariance was doneat all levels of the measurement model. Factor loading invariance means that the loadingsrepresenting each factor are equal and the unit of measurement of the underlying factoris identical. Intercept invariance represents the origin of the scale and intercepts of themeasured variable are equal. The first two levels are required for comparing latent meandifferences across groups (Widaman & Reise, 1997) and when achieved indicates thatscores from different groups have the same unit of measurement (factor loading) as well asthe same origin (intercept). If a tested model is found to be invariant at the first two levels(i.e., factor loadings and intercepts), it is generally accepted that the instrument is invariant(Vandenberg & Lance, 2000).

Results

None of the completed questionnaires had more than 12% (more than three items) missingitem responses from the constraints measure. For Time 1 and Time 2, all items exhib-ited normal distributions (skewness values = 0.58–1.95; kurtosis values = 0.10–3.30).Tests of multivariate normality had values under 2.0 (relative multivariate kurtosis



values = 1.01–1.91). Therefore, it is unlikely there was an inflated chi-square value causedby a non-normal distribution.

Baseline Models

We examined three potential baseline models (3-factor, 7-factor, and second-order) withmatched data for Time 1 and Time 2 collections. Fit indices for each measurement modelare reported in Table 2. The 3-factor model had poor fit, with CFI and TLI below cut-offvalues (.90) and RMSEA above the cut-off value (.05). The 7-factor model had the bestoverall fit compared to the other models with all indices in the acceptable range. Statisticalcomparison of the 7-factor model and the 3-factor model found that the 7-factor model wasa significantly better fitting model to the data (Change χ2 = 1229.480, Change df = 18,p < .001). The next best fitting model was the second-order model, but TLI was belowacceptable cut-off values in Time 1, and RMSEA was above an acceptable cut-off value inTime 2. Determination of what model was better when comparing the second-order modelversus the 7-factor models was based on fit indices. Results showed that the 7-factor modelwas a better fit to the data with higher CFI and TLI values and lower χ2/df and RMSEAvalues. Therefore, based on descriptive analysis of fit indices with the second-order modeland statistical analyses with the nested analysis of the 3- and 7-factor models we can inferthat the best fitting model was the 7-factor model. The 7-factor model was then used insubsequent analysis.

The results displaying factor structure underlying the 7-factor model for Time 1 andTime 2 are presented in Table 3. All factor loadings for each item were acceptable (<.40) andstandard errors were low (.088). Comparisons between the Time 1 and Time 2 showed thatthe factors loading/standard errors were similar. Factor reliabilities were in an acceptablerange with the exception of the “facilities” factor in both Time 1 (.680) and Time 2 (.692)data.

To assess multi-group factor validity, the measurement model was then tested with eachdemographic subgroup using CFA. Table 4 provides results of a thorough examination offit for the measurement model across time (Time 1 and Time 2), gender, grade level,race/ethnicity, and family SES. Fit for the entire sample in both collection periods wasacceptable for all indices. For gender, the male sample had poor fit (TLI and RMSEA) inTime 1 but acceptable in Time 2, while all indices were acceptable for females. With gradelevel, fit was acceptable for sixth and seventh grades while fit indices for the eighth grade

TABLE 2 Comparisons of Constraints Models

Model χ2 df χ2/df CFI TLI RMSEA

Fall Data Collection3-Factor Model 3675.366∗ 272 13.512 0..798 0.758 0.0797-Factor Model 1399.739∗ 254 5.511 0.932 0.913 0.0472nd Order Model 1770.900∗ 266 6.657 0.910 0.891 0.053

Spring Data Collection3-Factor Model 3641.798∗ 272 13.389 0.812 0.775 0.0787-Factor Model 1201.474∗ 254 4.730 0.947 0.932 0.0432nd Order Model 1718.412∗ 266 6.460 0.919 0.901 0.052

Note. ∗indicates p < .05, χ 2 = Chi-square, df = degrees of freedom, CFI = comparative fit index,TLI = Tucker Lewis fit index, RMSEA = root means square error of approximation.


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e2

Tim

e1

Tim

e2

Faci

liti

es.6

80.6

92T

hesp

ortf

acili

ties

are

poor

qual

ity.6

21.7

06.0

47.0

34.3

47.3

29.5

43.4

81T

hesp

ortf

acili

ties

are

notg

ood

enou

gh.7

05.7

22.0

46.0

42.3

29.3

30.5

74.5

44T

hesp

ortf

acili

ties

are

crow

ded

.580

.439

.046

.038

.721

.665

.275

.194

Acc

essi

bili

ty.6

99.7

09T

here

are

nosp

orts

near

my

hom

e.6

54.6

96.0

40.0

46.6

33.5

18.4

42.5

11I

dono

thav

etr

ansp

orta

tion

toge

tto

spor

ts.6

75.6

43.0

40.0

31.6

12.5

93.4

71.4

09I

cann

otaf

ford

the

mon

eyto

play

spor

ts.6

35.6

14.0

35.0

28.5

62.5

01.4

44.4

08Pa

rtne

rs.6

93.7

25M

yfr

iend

sdo

notl

ike

topl

aysp

orts

.579

.575

.030

.028

.648

.597

.297

.312

Ido

noth

ave

anyb

ody

topl

aysp

orts

with

.703

.785

.050

.055

.501

.398

.572

.636

Itis

diffi

cult

tofin

dot

hers

topl

aysp

orts

with

.713

.715

.050

.052

.475

.521

.578

.517

Not

e.∗ A

llst

anda

rdiz

edfa

ctor

load

ings

wer

esi

gnifi

cant

(p<

.05)

136


TAB

LE

4Fi

tInd

ices

byG

ende

r,G

rade

,Rac

e,Pa

rent

SES,

and

Spor

tPar

ticip

atio

nw

ithth

e7-

fact

orM

odel

Tim

e1

Col

lect

ion

Tim

e2

Col

lect

ion

Subg

roup

Nχ

2(2

54)

CFI

TL

IR

MSE

AN

χ2

(254

)C

FIT

LI

RM

SEA

Tota

lsam

ple

2029

1399

.739

∗.9

32.9

13.0

4720

2912

01.4

74∗

.947

.932

.043

Gen

der

Fem

ales

1019

775.

906∗

.939

.922

.045

1019

842.

714∗

.931

.912

.049

Mal

es98

210

08.5

82∗

.908

.882

.055

982

768.

38∗

.944

.928

.045

Gra

de6t

hgr

ader

s65

876

4.47

5∗.9

23.9

02.0

5065

863

8.02

9∗.9

32.9

14.0

487t

hgr

ader

s63

666

4.03

5∗.9

20.9

00.0

5063

666

5.63

5∗.9

28.9

08.0

508t

hgr

ader

s72

783

7.80

7∗.9

11.8

86.0

5672

774

9.98

5∗.9

27.9

07.0

52R

ace/

Eth

nici

tyW

hite

1043

1040

.462

∗.9

17.8

94.0

5510

4380

1.75

2∗.9

45.9

29.0

46B

lack

624

693.

431∗

.920

.890

.050

624

626.

520∗

.940

.920

.040

His

pani

c17

838

9.02

1∗.9

09.8

84.0

5517

848

7.41

5∗.8

52.8

11.0

73Fa

mil

ySE

SN

ofr

ee/R

educ

edlu

nch

1427

1129

.497

∗.9

29.9

09.0

4914

4510

00.6

14∗

.945

.930

.045

Free

redu

ced

lunc

h57

563

1.35

9∗.9

16.8

93.0

5155

660

9.40

8∗.9

16.8

93.0

50

Not

e.∗ i

ndic

ates

p<

.05;

bold

valu

esin

dica

tefit

indi

ces

belo

wcu

toff

crite

ria.

137



sample had some fit indices outside of cut-off criteria (TLI and RMSEA). For race/ethnicity,TLI was below cut-off criteria in Time 1 for all race/ethnic groups, while CFI, TLI, andRMSEA were below cut-off in Time 2 data with the Hispanic category. For family SES, fitwas acceptable for upper income respondents in Time 1 and both categories in Time 2, butTLI was low for the free-reduced lunch category in Time 1.

Invariance Tests

The 7-factor, baseline unconstrained model, was used to test invariance based on factorloadings, measurement weights, intercepts, structural covariance/variances, and measure-ment residuals by the time of data collection and the socio-demographic characteristics ofthe sample. In contrast to multigroup factor validity (Table 4), the findings do not relateto how the data fit the model but rather to how the respondents in each category (e.g.,males versus females) understood or interpreted the items. The changes in chi-square andchanges in fit statistics compared to an unconstrained model are shown in Table 5. Com-parison groups were considered invariant if there were nonsignificant differences in chisquare values and changes in TLI were less than .01 (Meade, Johnson, & Braddy, 2008).Invariance was found between Time 1 and Time 2, while all other comparisons showedsome indications of noninvariance at some level, particularly as the model became moreconstrained. Most non-invariance was found at the most constrained level (measurementresiduals). This was found with the sixth/seventh grade (Time 2), seventh/eighth grade,White/Black, White/Hispanic, Black/Hispanic (Time 2), and family income comparisons.The most evidence of noninvariance was found with the White/Black comparisons whereinvariance was found and the intercept level (Time 2) and variance/covariance level (Time1 and Time 2). Using criteria from Vandenberg and Lance (2000) and Chen, Sousa, andWest (2005), who suggested that only the factor loading and intercept invariance levelsneed to be met, our results display invariance with the 7-factor measurement model acrossall groups.

Discussion

The objectives of this study were to (1) compare three baseline models to examine the ten-ability of different factor structures associated with a constraint measure and (2) examinefactorial validity and invariance of the measure based on comparisons of socio-demographicsubgroups of adolescents and time periods. A 7-factor model (compared to a 3-factor model)exhibited a more appropriate measurement model based on fit indices and statistical com-parisons. Using the 7-factor model, construct validity and invariance of the model overtime were examined by gender, grade level, race/ethnicity, and socioeconomic status. Wefound the model to be invariant at the factor loading and intercept levels, while there wassome noninvariance at further constrained levels. In general, the 7-factor model exhib-ited psychometric stability, providing evidence of its utility over a range of demographicsubgroups.

Findings related to the first study objective suggest several implications for futureresearch. First, the first model (the 3-factor model) was based on the three theoreticaldimensions formulated by Crawford et al. (1991). This model yielded a poor fit which likelyresulted from model misspecification. Researchers that consider using a 3-factor model asa basis for segmentation or that examine constraints in relation to participation or otherpsychological constructs (e.g., negotiation) should carefully consider their measurementstrategy.


TAB

LE

5In

vari

ance

Test

sof

the

7-fa

ctor

Mod

elB

ased

onSo

cio-

dem

ogra

phic

Gro

ups

Tim

e1

Dat

aC

olle

ctio

nT

ime

2D

ata

Col

lect

ion

Com

pari

son

Gro

upχ

2C

FIT

LI

RM

SEA

�χ

2�

df�

TL

Iχ

2C

FIT

LI

RM

SEA

�χ

2�

df�

TL

I

Fall

/Spr

ing

Unc

onst

rain

ed26

01.2

12.9

40.9

23.0

32M

easu

rem

entw

eigh

ts26

36.3

03.9

39.9

25.0

3135

.091

∗18

.002

Mea

sure

men

tint

erce

pts

2674

.699

.939

.928

.031

73.4

87∗

43.0

05St

ruct

ural

cova

rian

ces

2759

.763

.937

.930

.030

158.

551∗

71.0

07M

easu

rem

entr

esid

uals

2965

.015

.932

.927

.031

363.

803∗

96.0

04M

ales

/Fem

ales

Unc

onst

rain

ed17

84.4

92.9

24.9

02.0

3516

11.0

97.9

38.9

21.0

33M

easu

rem

entw

eigh

ts18

24.3

47.9

22.9

04.0

3539

.855

∗18

.000

1657

.649

.936

.921

.033

46.5

52∗

18.0

00M

easu

rem

enti

nter

cept

s19

32.7

56.9

17.9

02.0

3514

8.26

4∗43

.000

1904

.709

.924

.910

.035

293.

612∗

43.0

00St

ruct

ural

cova

rian

ces

2002

.001

.915

.904

.035

217.

509∗

71.0

0220

18.7

47.9

19.9

09.0

3540

7.65

∗71

.011

Mea

sure

men

tres

idua

ls21

26.7

76.9

09.9

02.0

3634

2.28

4∗96

.000

2284

.732

.905

.898

.037

643.

635∗

96.0

236t

h/7t

hG

rade

Unc

onst

rain

ed14

28.5

09.9

12.8

87.0

3713

03.6

65.9

30.9

11.0

35M

easu

rem

entw

eigh

ts14

57.0

82.9

11.8

90.0

3728

.573

18.0

0313

45.5

54.9

28.9

11.0

3541

.889

∗18

.002

Mea

sure

men

tint

erce

pts

1504

.384

.909

.892

.037

75.8

75∗

43.0

0513

94.1

73.9

26.9

13.0

3490

.508

∗43

.004

Stru

ctur

alco

vari

ance

s15

48.1

16.9

07.8

96.0

3611

9.60

7∗71

.009

1482

.732

.921

.911

.035

179.

067∗

71.0

08M

easu

rem

entr

esid

uals

1610

.533

.903

.896

.036

185.

024∗

96.0

0915

48.9

18.9

17.9

11.0

3524

5.25

3∗96

.016

6th/

8th

Gra

deU

ncon

stra

ined

1602

.283

.906

.880

.039

1388

.011

.929

.910

.036

Mea

sure

men

twei

ghts

1630

.148

.905

.883

.039

27.8

6518

.003

1412

.165

.929

.912

.035

24.1

5418

.000

Mea

sure

men

tint

erce

pts

1677

.623

.903

.886

.038

75.3

40∗

43.0

0614

56.5

33.9

27.9

14.0

3568

.522

∗43

.002

Stru

ctur

alco

vari

ance

s17

33.6

7.9

01.8

88.0

3813

1.38

7∗71

.008

1522

.456

.924

.915

.034

134.

445∗

71.0

05M

easu

rem

entr

esid

uals

1814

.47

.896

.888

.038

212.

187∗

96.0

0815

84.2

97.9

21.9

15.0

3419

6.28

6∗96

.008

7th/

8th

Gra

deU

ncon

stra

ined

1501

.835

.916

.893

.038

1415

.619

.928

.907

.036

Mea

sure

men

twei

ghts

1533

.643

.915

.895

.038

31.8

08∗

18.0

0214

40.5

81.9

27.9

10.0

3624

.962

18.0

01(C

onti

nued

onne

xtpa

ge)

139


TAB

LE

5In

vari

ance

Test

sof

the

7-fa

ctor

Mod

elB

ased

onSo

cio-

dem

ogra

phic

Gro

ups

(Con

tinu

ed)

Tim

e1

Dat

aC

olle

ctio

nT

ime

2D

ata

Col

lect

ion

Com

pari

son

Gro

upχ

2C

FIT

LI

RM

SEA

�χ

2�

df�

TL

Iχ

2C

FIT

LI

RM

SEA

�χ

2�

df�

TL

I

Mea

sure

men

tint

erce

pts

1578

.002

.913

.898

.037

76.1

67∗

43.0

0514

99.8

28.9

24.9

11.0

3684

.209

∗43

.004

Stru

ctur

alco

vari

ance

s16

31.2

96.9

11.9

00.0

3712

9.46

1∗71

.007

1549

.001

.923

.913

.035

133.

382∗

71.0

05M

easu

rem

entr

esid

uals

1696

.166

.908

.901

.036

194.

331∗

96.0

0816

45.5

31.9

17.9

11.0

3622

9.91

2∗96

.011

Whi

te/B

lack

Unc

onst

rain

ed17

33.9

220.

915

0.89

1.0

3814

28.3

28.9

39.9

21.0

33M

easu

rem

entw

eigh

ts18

16.0

340.

910.

889

.038

82.1

12∗

18.0

0214

96.1

05.9

35.9

20.0

3467

.777

∗18

.004

Mea

sure

men

tint

erce

pts

1995

.81

0.89

90.

881

.040

261.

888∗

43.0

1016

54.1

26.9

26.9

13.0

3522

5.79

8∗43

.013

Stru

ctur

alco

vari

ance

s21

46.1

120.

891

0.87

7.0

4041

2.19

∗71

.014

1828

.514

.917

.906

.037

400.

186∗

71.0

22M

easu

rem

entr

esid

uals

3160

.619

0.82

20.

808

.050

1426

.697

∗96

.083

2648

.634

.864

.853

.046

1220

.306

∗96

.075

Whi

te/H

ispa

nic

Unc

onst

rain

ed14

30.3

340.

916

0.89

2.0

3912

90.6

2.9

32.9

13.0

36M

easu

rem

entw

eigh

ts14

68.6

710.

914

0.89

4.0

3838

.337

∗18

.002

1311

.647

.932

.916

.036

21.0

2718

.000

Mea

sure

men

tint

erce

pts

1555

.057

0.90

80.

892

.039

124.

723∗

43.0

0014

13.9

12.9

25.9

11.0

3612

3.29

2∗43

.007

Stru

ctur

alco

vari

ance

s16

70.7

360.

90.

888

.039

240.

402∗

71.0

0414

81.4

42.9

22.9

12.0

3619

0.82

2∗71

.010

Mea

sure

men

tres

idua

ls20

76.4

720.

866

0.85

5.0

4564

6.13

8∗96

.037

1865

.66

.890

.882

.042

575.

04∗

96.0

43B

lack

/His

pani

cU

ncon

stra

ined

1083

.055

0.91

0.88

4.0

3811

14.9

57.9

09.8

83.0

39M

easu

rem

entw

eigh

ts11

13.6

570.

908

0.88

6.0

3730

.602

∗18

.002

1132

.806

.909

.887

.038

17.8

4918

.000

Mea

sure

men

tint

erce

pts

1186

.882

0.9

0.88

2.0

3810

3.82

7∗43

.002

1194

.366

.903

.886

.039

79.4

09∗

43.0

06St

ruct

ural

cova

rian

ces

1226

.452

0.89

80.

886

.037

143.

397∗

71.0

0212

58.1

81.8

98.8

85.0

3914

3.22

4∗71

.009

Mea

sure

men

tres

idua

ls12

79.5

30.

894

0.88

6.0

3719

6.47

5∗96

.002

1313

.142

.893

.885

.039

198.

185

96.0

16F

ree

orre

duce

dlu

nch/

No

free

lunc

hU

ncon

stra

ined

1760

.987

0.92

50.

904

.035

1610

.202

.938

.921

.033

Mea

sure

men

twei

ghts

1819

.139

0.92

30.

905

.035

58.1

52∗

18.0

0116

30.9

61.9

38.9

24.0

3220

.759

18.0

00M

easu

rem

enti

nter

cept

s19

51.6

780.

916

0.90

1.0

3619

0.69

1∗43

.003

1766

.533

.932

.920

.033

156.

331∗

43.0

06St

ruct

ural

cova

rian

ces

2047

.03

0.91

20.

902

.036

286.

043∗

71.0

0218

63.9

92.9

28.9

19.0

3325

3.79

∗71

.010

Mea

sure

men

tres

idua

ls26

36.0

550.

879

0.86

9.0

4187

5.06

8∗96

.035

2467

.386

.896

.888

.039

857.

184∗

96.0

42

Not

e.∗ i

ndic

ates

p<

.05;

bold

valu

esin

dica

tefit

indi

ces

belo

wcu

toff

crite

ria.

140



Second, the 7-factor model exhibited greater separation between interpersonal andstructural constraints items (see Figure 1). The 7-factor model showed acceptable fit indicesoverall and, because both the 3- and 7-factor models were nested, statistical comparisonestablished acceptable measurement properties for the 7-factor model. This could indicatethat specification is a problem with the 3-factor theoretical model. For example, items meantto measure accessibility, facilities, and time may elicit varied responses. One respondentmay not perceive high time constraints but rather perceive high accessibility constraints.Another respondent may perceive and report the exact opposite. In the 3-factor modelstructure, this variation leads to measurement inconsistencies since we are specifying in themodel that these constraints relate (or account for common variance) to each other. Thisissue has also been noted by Hubbard and Mannell (2001), who explained there should beno expectation of strong intercorrelations within a dimension. Therefore, while the separatestructures may be theoretically related their practical association is untenable.

A third implication for future research relates to the second-order model. It was notthe best fitting measurement model, but it did provide evidence that supports the theoretical3-dimensional structure of constraints and how multiple factors reflect the three theoreticaldimensions. The second-order model measured the 3- and 7-factor models together. Theresults showed that the three distinct first-order factors (i.e., accessibility, facilities, andtime) were hierarchically linked to a second-order factor (i.e., structural constraint). Inessence, this model accommodates and accounts for specification issues found in the 3-factor model. We found acceptable fit for this model, but the 7-factor model exhibited asuperior fit. The model results provide evidence that the first-order factors are correctlyspecified to the theoretical structure.

Finally, based on the model comparisons in the current study, future studies shouldmeasure constraints at the more practical (first-order) level. Nearly all constraint studiesanalyze factor means or totals. If factor means are derived from the theoretical level,much of the information can be lost, and as other studies have shown, internal reliabilitiesof the factors may be low. More detailed specification can be used such as the 7-factorstructure in this study. As seen in the second-order model, specification with multiple factorscan be related back to the theoretical structure. Furthermore, studies that use structuralequation models can determine if factors added to a constraint instrument (based on thespecifics of the population or leisure context) truly measure and are associated with thetheoretical dimensions. For example Loucks-Atkinson and Mannell (2007) developed aspecific constraint category, pain-coping techniques, for a population who had fibromyalgiasyndrome, which was used within a constraint-negotiation model.

The second study objective focused on measurement invariance and used four con-strained levels of the baseline 7-factor model. Each socio-demographic category was thencompared and evaluated based on each invariance level. These comparisons providedevidence of the equivalence of constraint measures when comparing groups that differ ac-cording to gender, grade level, race/ethnicity, SES, and by time. Traditional psychometricevaluations (e.g., internal reliability, predictive validity) are important but not completelysufficient in determining if an instrument is measuring equivalently between groups. In-variance tests the extent to which an instrument is measuring a factor or its operations(e.g., factor loadings) equivalently (Paxton et al., 2008). If invariance is not tested, thereis increased risk of comparing subgroups on nonequivalent measures leading to inaccurateinterpretation of study results (Motl et al., 2000). We performed a thorough assessment byexamining all four levels of invariance (factor loadings, intercepts, variances, and error).Our findings indicate that all models met invariance standards at the factor loading andintercept levels (first two levels). Achieving invariance standards at these levels indicatesthat factor means can be compared across subgroups of respondents groups (Chen et al.,



2005). In regards to our data, if we found differences in constraint factors (at the constructlevel) based on gender, there is strong evidence that the results were group differences (boysand girls differ on the construct) and not a measurement artifact (e.g., they interpreted theconstruct items differently). Our study provides initial evidence that constraint factors,when applied to sport participation, can be measured similarly between groups that differaccording to gender, grade level, race, and family SES.

Turning to the third and fourth levels of invariance (variance-covariance and error),signs of noninvariance in some of our subgroup comparisons were observed. For example,noninvariance was observed at three levels in comparisons of White and Black adolescents.The extent of noninvariance was not found in other contrasts of race/ethnicity. Althoughpsychometric scholars (e.g., Vandenberg & Lance, 2000) have noted that noninvariancewill be found as a model is more constrained, our results indicate that future studiesinvestigating race/ethnicity differences, particularly White and Black comparisons, shouldtest for invariance.

To assess longitudinal stability, model comparisons, the factorial validity, internalreliability, fit indices for subgroups, and invariance in both Time 1 and Time 2 wereexamined. In general, more similarities than differences in model fit and factor loadingsbetween the Time 1 and Time 2 data were found. There was a trend of better fit and higherfactor loadings with the Time 2 data. This was also the case for internal reliabilities. Further,CFA based on socio-demographic categories found 6 of 12 CFAs in Time 1 had at least onepoor fit index, while in Time 2 only two of the 12 comparisons had at least one poor fit index.The improved factor loadings, fit indices, and reliability coefficients may be evidence oflearning associated with administering an identical instrument to the same respondents morethan once. While the findings provide evidence of temporal stability over nine months, theycannot be compared directly with previous studies that examined constraints longitudinallywith adults and over longer periods of time (Jackson & Witt, 1994; Mowen et al., 2005;Wright et al., 2001). However, findings from the current study are consistent with earlierstudies showing stability over time. Researchers with longitudinal data sets are encouragedto undertake more stringent tests of measurement models and invariance.

Conclusions

Constraints to leisure have been widely studied in a variety of participant groups and envi-ronmental settings. Moreover, theoretical understanding related to the nature of constraintsand constraint processes has increased and the development and evaluation of measures isa pressing need (Crawford & Jackson, 2005). Despite the rapid emergence of constraintsresearch, there have been limited empirical studies of measurement properties of constraintmeasures. A quantitative approach requires confidence that an instrument accurately mea-sures the phenomenon under study. While the items related to constraints instrumentationhave been modified or even customized to the population and/or activity and measurementrelated to number factors has differed, measurement within the theoretical framework hasbeen relatively consistent. For example, the items used in Crawford and Jackson’s 1987study are similar to the items used by Alexandris et al. (2008), Shores et al. (2007), andSon et al. (2008). This current study afforded an opportunity to examine these quantitativemeasures in greater depth and scope recognizing that there may be subtle changes relatedto constraints instrumentation.

Giving attention to psychometric issues can enhance data quality and lend confidence toresults from measures applied across different population subgroups (Crawford & Jackson,2005). While traditional psychometric evaluations (e.g., internal consistency, predictive



validity) are important, they are not sufficient in determining whether a factor is being mea-sured equivalently between groups. Prior studies (e.g., Mowen et al., 2005; Shinew et al.,2004; Shores et al., 2007) report differences in constraints based on socio-demographicgroups. To our knowledge, there has been no research that has investigated the appropriate-ness of using constraints measures among middle school-aged adolescents for comparisonsinvolving demographic subgroups or over time. Therefore, this study fills an important gapin the literature by providing evidence related to model specification, factorial validity, andmultigroup invariance of perceived constraints.

There are several limitations and directions for further research. The first limitationrelates to the instrument used in our study. As noted, there are several variations of theinstrument. We chose an instrument that had been found to be valid within a recreationalsport context. Our findings may not extend to other constraint instruments that use differentitems. Second, this instrument had only one factor that related to intrapersonal constraints,so the findings (especially the baseline model comparisons) may not be valid with in-struments that have multidimensional factors related to intrapersonal constraints. Third,our results were with middle school students and may not be representative of all middleschool students. Also, adolescents from Asian-American or Native American backgroundswere not included in this study. Additional comparisons based on a wider age group ordevelopmental stage were not assessed in our study and are certainly still needed. Fourth,the longitudinal analysis was conducted over a nine-month time frame, and studies that usepanel data over a longer time frame are needed. Finally, our findings may differ dependingon the leisure activity and/or setting. Strengths of the study include the size and diversity ofthe sample, the high response rate, and the comprehensive and rigorous psychometric test-ing. It is important to recognize that our study focuses solely on a quantitative assessment ofconstraints. One strength of qualitative methodologies is the ability to discern the existenceand meaning of constraints in normal, everyday leisure among of youth (Samdahl, 2005;Samdahl & Jekubovich, 1997). We encourage other researchers to pursue complementarystrategies to shed additional light on the nature of constraints in leisure and sport.

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Measurement Properties of Constraints to Sport Participation: A Psychometric Examination with Adolescents