erni masdupi_ok

BUSINESS DIVERSIFICATION, COMPANY SIZE AND COMPANY PERFORMANCE: A MEASUREMENT MODEL APPROACH

Erni Masdupi

Abstract : This study assesses the construct validity of the measurement model of diversification of business, company size and company performance of listed companies in Indonesia Stock Exchange (IDX) in the period of 1996 to 2005. Its objective is to examine the fitness of the hypothesized measurement model on the data collected. To answer the research questions, Structural equation modeling (SEM) is employed. By using 210 company-year observations, it is found that the hypothesized measurement model fits the data as shown by the goodness of fit indices and the significant factor loadings. Indicators of diversification of business had the significant factor loadings with their values were more than 0.3. This indicates that all measures could manifest diversification of business. Although all are significant but the number of business segments is the most important because it has a higher factor loading. Moreover, company size could be explained by its manifests since the factor loadings of the natural log of total assets, the natural log of sales and the natural log of MVE are significant and more than 0.3. This indicates that convergent validity was achieved. Nevertheless, among the three indicators representing company size, the natural log of total assets represents company size better than other indicators. Finally, all indicators of company performance are also significant and could achieve cut of value. This would mean that company performance could be explained by its indicators, but market-based measure (MBVR) is closely linked to company performance because it has a higher factor loading.

Key words: the measurement model, diversification of business, company size, company performance, just-identified, goodness of fit indices and the factor loadings.

This study examines the construct validity of the measurement model of business diversification, company size and company performance of listed companies on Indonesia Stock Exchange (IDX). Many more studies have measured them directly observed variables (Berger & Ofek, 1995; Lang & Stulz, 1994; Lemmon & Lins, 2003; Rogers et al., 2008; Zeitun & Tian, 2007), it was thought that as latent constructs, this was hoped to give a fresh and insightful set of findings that may be different from these using the mainstream and entrenced way of measuring the variables. Therefore, this study has three latent variables or three constructs as follows: business diversification, company size and company performance.

This article is organized into five sections. Section one presents the introduction of the study. The following section explains literature review and model fit and section three provides the methodology. Analysis of data and research findings are presented in section four. This article ends with conclusions and recommendations.

Literature Review of Confirmatory Factor Analysis

CFA plays an important role in SEM to validate the measurement model (Anderson & Gerbing, 1982). This step exhibits a test of measurement model with the objective to achieve the confirmatory assessment of nomological validity (i.e. checking whether the measurement of construct is consistent with the conceptualisation in this study). Then, it is followed by testing the significance of the hypothesized relationship among constructs through the structural model. Nevertheless, this paper only focused on the measurement model of business diversification, company size and company performance.

The measurement model is highly recommended to be predicted before the testing of a structural model. It is evaluated by using goodness-of-fit (GOF) measures. CFA has essential functions such as to examine the factor loadings in every dimension in forming a variable, to confirm that the indicators/dimensions sort themselves into factors corresponding to how the researcher has linked the indicators to the latent variables and to

2 Jurnal Economac, Volume 11, Nomor 2, Oktober 2011, hlm 1-7

assess the role of measurement error in the model. The aim of CFA is to analyze how well the manifests/indicators/dimensions can each explain their latent variable.

In the measurement model, a confirmatory measurement model should be developed for scale purification and assessing the psychometric properties of measures with the purpose of examining the construct validity (convergent and

discriminant validity) and reliability of measures. Measurement model is only for the latent variables. Therefore, specification of the first measurement model is diversification of business as described in Figure 1 where equations can be derived for this as follows.HI_Sales = λ1Diversification + e1

HI_Assets = λ2Diversification + e2

No_Segment = λ3Diversification + e3

Figure 1. Measurement Model of Diversification of Business

The second measurement model is company size which is visualized in Figure 2. The measurement model can be converted to equations as follows.LnAssets = λ4 Size + e4

LnSales = λ5 Size + e5

LnMVE = λ6 Size + e6

Figure 2 Measurement Model of Company Size

The last measurement model is for the company performance which has three indicators as described in Figure 3. The equations for this measurement model are:ROE = λ7 Company Performance + e7

ROA = λ8 Company Performance + e8

MBVR = λ9 Company Performance + e9

Diversification

No_Segmente3

1

HI_Assetse21

HI_Salese11

1

Size

LnMVEe6 1

1

LnSalese51

LnAssetse41

Erni Masdupi, Business Diversification... 3

Figure 3Measurement Model of Company Performance

Overall Model Fit Indicator

After the measurement model is validated, the model fit should be assessed to identify the degree to which the specified indicators represent hypothesized constructs in the CFA and path coefficients of hypothesized relationships between theoretical constructs in SEM. Measurement model validity depends on GOF for the measurement model and specific evidence of construct validity. GOF indicates how well the specified model reproduces the covariance matrix among the indicator items (Hair, Black, Babin, Anderson & Tatham, 2006).

Each GOF measure is unique but the measures are classified into three general groups: (1) absolute measures; (2) incremental measures; and (3) parsimony fit measures. The absolute fit measures determine the predicted level of the overall fit (structural and measurement), while the incremental fit measures compare the proposed model with the basic model (called “null model” or independent model”). Lastly, the parsimonious fit measures adjust the measures of fit to provide a comparison between models with differing numbers of estimated coefficients, the purpose being to determine the amount of fit achieved by each estimated coefficient. When assessing the SEM model, not all GOF will be used, as long as some of them have fulfilled the requirement, the model is considered fit (Hair et al., 2006). Table 1 summarizes acceptance or rejection of the GOF indicators/measures.

The chi-square is absolute fit index that is quite sensitive to sample size and complexity. Therefore, rejection of a model on the basis of this evidence alone is inappropriate (Bagozzi & Yi, 1988). Hence, other measures to assess the model fit were used. Goodness-of-fit index (GFI) does not depend on the sample size explicitly (Joreskog & Sorbom, 1989) and it is equal to R

square in a regression; whereas the root mean square error approximation (RMSEA) incorporates no penalty for model complexity and tends to favor models with many parameters (Steiger, 1990). Down the list is incremental fit index such as Tucker Lewis index (TLI) and comparative fit index (CFI), which are also not sensitive to sample size (Ferdinand, 2006). Finally, normed chi-square (CMIN/DF), a parsimony fit index suggests a ratio approximately five or less (Wheaton, Muthen, Alwin, & Summers, 1977).

Besides GOF measure, SEM can examine the accuracy of measurement by assessing the construct validity of proposed measurement theory. For SEM, construct validity is used to assess the validity of proposed measurement theory by checking the extent to which a set of observed items reflect the theoretical latent construct (Hair, Black, Babin, Anderson, & Tatham, 1998). Convergent validity is a common measurement for SEM by determining the factor loadings, standardized factor loadings, variance extracted and critical ratio. If the standardized factor loading is more than 0.3 (Tabachnick & Fidell, 2007), variance extracted is more than 0.5 (Hair et al., 2006) and critical ratio is double the standard error (Anderson & Garbing, 1988 as cited in Ferdinand (2006)), it shows convergent validity. The size of the factor loading is one important consideration. In the case of high convergent validity, high loadings on a factor/latent would indicate they converge on some common point (Hair et al., 2006). In other words, all indicators could converge into their latent variable as suggested by the theory. Only a valid construct could result in a better fit in the measurement model and it would influence the result of hypothesis testing. In brief, once the measurement model could achieve the construct validity, the measurement

CompanyPerformance

ROE e711

ROA e81

MBVR e91


model would provide a better fit of the data collected in this study. In addition, construct reliability assesses convergent validity of the latent variable. If construct reliability is more

than 0.7, it indicates that convergent validity is achieved (Hair et al., 2006).

Table 1Summary of GOF Indicators

GOF Indicators/MeasuresAcceptable Fit

LevelDescription

A. Absolute Fit Measures

Chi-Square (χ2)Statistic/ Probability level

ρ value ρ ≥ 0.05 Empirical data is identical with the theory/model so null hypothesis is accepted. ρ ≥ 0.05

Goodness of Fit Index GFI Value ≥ 0.90 0 (poor fit) to 1 (perfect fit); ≥ 0.90 = good fit; 0.80 ≤ GFI ≤ 0.89 = marginal fit

Root Mean Square Error of Approximation

RMSEA Value ≤ 0.08<0.05 a very close fit

RMSEA ≤ 0.08 indicates reasonable error of approximation; while a value > 0.10 = significant problem

B. Incremental Fit Measure

Adjusted Goodness of Fit Index

AGFI Value ≥ 0.90 Value adjusted for AGFI ≥ 0.9 = good model fit; 0.80 ≤ AGFI< 0.89 = marginal fit

Tucker-Lewis Index TLI Between 0-1

TLI ≥0.9 = good fit;0.80 ≤ TLI < 0.89 = marginal fit

Comparative Fit Index CFI Value ≥ 0.8 Value close to 1 indicates a very good fit; ≥ 0.9 = Good model fit; 0.8 ≤ CFI < 0.89 = marginal fit

C. Parsimonious Fit Measures

Normed Chi-Square CMIN/DF(χ2/df)

Low bound = 1.0High bound = 2.0 or 3.0 till 5.0

Ratio between Chi-square and degree of freedom

Source: (Ghozali & Fuad, 2005; Hair et al., 2006; Marsh & Hocevar, 1985; Wheaton et al., 1977)

Furthermore, discriminant validity indicates that the latent variables are different from each other. In other words, individual measured items (indicators) should represent only one latent construct and they do not explain other constructs. When the discriminant validity is achieved, it means that all the constructs are different (unique) and the CFA fit would be good. As such, when the correlation among latent variables is less than 0.9, it shows discriminant validity. In practice, however, this test does not always provide a strong evidence of discriminant validity, because high correlations, sometimes as high as 0.9, can still produce significant differences in model fit (Hair et al., 2006). Therefore, Hair et al. (2006) suggested that a

better test is to compare the variance extracted percentages for any two constructs with the square of the correlation estimated between the two constructs. If the variance extracted estimates for two constructs is greater than the square of the correlation between the two constructs, it provides an evidence of discriminant validity. This would mean a latent construct could explain its indicators better than it explains another construct.

METHODOLOGY

The secondary data was used in this study which come from the annual reports of listed companies on the IDX in the period of


1996 to 2005 financial years. Based on the purposive sampling, 215 company-year observations were selected with a set of criteria as follows: (1) non-financial companies, (2) the availability of financial statements during the analysis period which included earnings before interests and taxes, earning after taxes, sales, total assets, and the number of business segments.

SEM was employed in this study. It is famous as a two-step approach in which the measurement model through confirmatory factor analysis (CFA) was done before doing the structural model (Anderson & Gerbing, 1988) with the objective to assess the validity of construct and the model fit. According to SEM,

observed variables are simbolized by rectangle and unobserved/latent variables were indicated by a symbol ‘oval’. Endogenous variables and exogenous vaiables refer to dependent variables and independent variables in regression respectively. In this study, the observed endogenous variables included ROE, ROA, MBVR, HI_Sales, HI_Assets, NoSegment, LnAssets, LnSales, and LnMVE while unobserved exogenous variables are as follows: diversification of business, company size, company performance, e1, e2, e3, e4, e5, e6, e7 e8, and e9. Measurement of each variable is showed in Table 2.

Table 2: Variables in this study and their measurementVariable DescriptionCompanyPerformanceROEit

ROAit

MBVRit

BusinessdiversificationHI_Sales

HI_Assets

NoSegment

CompanysizeLnAssets

LnSales

LnMVE

eRes

Company performance is measured by return on equity, return on total assets and market to book value ratio.Return on equity company i at year t; ratio between net earning and equity (Chen & Ho, 2000; Cui & Mak, 2002; Demsetz & Villalongga, 2001; Kumar, 2005; Randoy & Goel, 2003; Rogers et al., 2008; Short & Keasey, 1999).Return on total assets company i at year t; ratio between earnings before interest and taxes (EBIT) and total assets (Li et al., 2006; Moh’d et al., 1998; Titman & Wessels, 1988; Zeitun & Tian, 2007).Market to book value ratio company i at year t; ratio between market value and book value (Kumar, 2005; Short & Keasey, 1999; Zeitun & Tian, 2007)(Kumar, 2005; Short & Keasey, 1999; Zeitun & Tian, 2007).Business diversification is represented by Herfindahl index by sales, Herfindahl index by total assets, and the number of business segments.Herfindahl index by sales is sum of squared value of sales per segment as a fraction of company sales (Lang & Stultz, 1994); value 1 indicates undiversified company and value is close to zero, it shows diversified company.Herfindahl Index by assets (HI_Assets) is sum of squared value of assets per segment as a fraction of company assets (Lang & Stultz, 1994); value 1 indicates undiversified company and value is close to zero, it shows diversified company.Segment is number of business segments of company (Berger & Ofek, 1995; Chen & Ho, 2000; Denis et al., 1997; Lang & Stultz, 1994).Compan size is manifested by the natural log of total assets, the natural log of sales, andthe natural log of market value of equity (MVE).LnAssets is the natural log of total assets (Li et al., 2006; Mitton, 2002; Serrano-Cinca et al., 2007).Lnsales is measured as the natural log of sales (Kumar, 2005; Mitton, 2002; Titman & Wessels, 1988).LnMVE is the natural log of MVE. Market value of equity is measured as common stock outstanding multiply by closing price at the fiscal year end (Hull, Mazakech, & Ockree, 1998).ErrorResidual

Following the work of Bowden (2000), Li et al. (2006), Serrano-Cinca et al. (2007), and Titman and Wessels (1988), diversification of business, company size and company performance are considered to be latent variables. Each latent construct has only three indicators. This study could use more indicators to represent each construct but since the number of sample in this study is rather limited, this study has selected

the three indicators. This study could determine which indicators were closely link to business diversification, company size and company performance.

The first latent variable is the diversification of business, which cannot be observed directly, but it can be observed through its dimension represented by Herfindahl index by sales, Herfindahl index by total assets and the


number of business segments. Company size is the second latent variable, which is measured by natural log of total assets, natural log of sales and natural log of MVE. The third latent variable is company performance. Based on previous studies, it is found that performance as a latent variable had been employed by Filatotchev et al. (2007), Li et al. (2006), Sarapaivanich and Kotey (2006), Serrano-Cinca et al. (2007), and Shen et al. (2006). Company performance is manifested through three indicators that show current performance (ROE and ROA) and market or

future performance (MBVR). The use of dimensions or indicators in the three constructs could improve statistical estimation (Hair et al., 2006). In this case, SEM could assess the contribution of each indicator in representing its associated construct, and measure how well a set of indicators represents the construct (its reliability), which could then be incorporated into the estimated relationships between the constructs. Table 3 summarizes the variables in this study.

Table 3Variables in This Study

Multivariate outliers were tested by Mahalanobis distance (less than 34.528, p < 0.001) and normality data were assessed (skewness divided by the standard error is less than 2.58, p < 0.001), both were conducted before the main analysis was run (Tabachnick & Fidell, 2007). Five outlier cases were excluded; hence the final data become 210 company year observations. The variables with non-normally distribution were transformed through squared root (sqrt/sq/rsq) and natural log (Ln) depending on the severity of skewness (Manning & Munro, 2004) in order to achieve the normality assumption. If data transformation caused other problems such as missing values, they were replaced by their mean in order to fulfill the assumption of SEM.

CFA was executed for each latent variable - diversification of business, company size and company performance, by using AMOS 7 program. It was found that the latent variables with three indicators resulted in a just-identified model (zero degree of freedom). This means the number of data covariance and variances equals to the number of parameters to be estimated. A just-identified model could not be analyzed. It is not scientifically interesting because it has no degree of freedom. Therefore, it can never be

rejected (Byrne, 2001). In other words, the model is perfect. However, SEM would need an over-identified model or a positive degree of freedom (Byrne, 2001) where the number of estimated parameters must be less than the number of data points (variance and covariance of the observed variable) so that the parameters could be estimated. To get an over-identified model, for the latent constructs with three indicators, CFA must be conducted together (Byrne, 2001) such as for diversification and company size. To ensure that the measurement models were valid and fit, an overall measurement model/CFA was also executed for all latent variables This is because each CFA would provide different results in construct validity and model fit.

Model is modifed based on modification indices (MI) which is supported by the related theories. Its objective is to improve the model fit through adding or deleting estimated parameters from the original model or correlate among indicators.Chi-square will be reduced as much as modification indices value when model modification is conducted (Byrne, 2001). For example, MI value of NoSegment and LnSales is 10.23. This would mean that the chi-square would fall by at least 10.23. This study needs a lower and insignificant chi-square to indicate that

Construct Description Dimension of Construct

Diversification of Business

Latent variable Herfindahl index by sales (HI_Sales)

Herfindahl index by total assets (HI_Assets)

Number of business segments (No_Segment)

Company Size Latent variable Natural log of total assets (LnAssets)

Natural log of total sales (LnSales) Natural log of MVE (LnMVE)

Company Performance

Latent variable ROE ROA MBVR


the model fits the data collected of listed companies on IDX. Results of Analyses

This study showed that the number of distinct sample moments were 21 and the number of distinct parameters to be estimated were 15; as a result, the number of degree of freedom was 6 (21-15). This indicated that the model is over identified and could be analyzed.

Figure 4 showed CFA for Diversification of Business and Company Size. All indicators had standardized loading of more than 0.3 and statistically significant at 0.01 level (critical ratios - C.R > 1.96) with minimum and maximum value of -0.69 and 0.86, respectively. Hence, it shows that all indicators can explain their latent variable (Tabachnick & Fidell, 2007) and this model could fulfill convergent validity. Specifically, diversification of business with

three indicators, Herfindahl index by sales, Herfidahl index by total assets and number of segments, had factor loadings of -0.69, -0.79 and 0.85, respectively. Although all indicators are significant, among the three indicators representing diversification of business, the number of business segments is the most important because it has a higher factor loading (0.85). The natural log of sales, the natural log of total assets and the natural log of market value of equity as indicators of company size had standardized factor loadings of 0.85, 0.86 and 0.71, respectively. It shows that all indicators could explain company size. Nevertheless, the natural log of total assets is closely linked to company size since its factor loading is higher (0.86). In brief, all factor loadings exceeded the standardized factor loading of SL > 0.3, which fulfills the requirement of measurement model for diversification of business and company size.

Figure 4CFA for Diversification of Business and Company Size

The results of critical ratio (C.R) of each indicator also shows the convergent validity is achieved because the critical ratios were double the standard error (SE) (Anderson & Gerbing (1988) as cited in Ferdinand (2006)). This is consistent with the result of standardized factor loadings. Specifically, for the diversification of business, the values were Herfindahl index by

sales (SE = 0.02, C.R = -9.87); Herfindahl index by assets (SE = 0.05, C.R= -10.71). For the latent company size, standard error and critical ratio for each indicator are as follows: the natural log of sales (SE = 0.17, C.R= 11.07); and the natural log of assets (SE = 0.65, C.R= 11.06).

Besides standardized factor loadings and critical ratio, construct reliability and variance

Diversification ofBusiness

.73

NoSegment_sqrte3

.85

.62

HI_Assetse2-.79

.48

HISales_sqe1-.69

Size

.51

LnMVE_sqrte6

.71

.74

LnAssetse5.86

.72

LnSales_sqe4.85

.35.29

.19

Standardized estimates Goodness-of- fit indeces:

Ratio: 2.578; Prob: .017; GFI: .976; CFI: .983; TLI: .957; RMSEA: .080


extracted could also achieve convergent validity of the latent variables because their values were more than the cut off points (construct reliability > 0.7; variance extracted > 0.5). Construct reliability and variance extracted were 0.82 and 0.61 for diversification of business and 0.85 and 0.66 for company size. This result is consistent with standardized factor loadings and critical ratios.

Convergent validity for CFA of diversification and company size could be satisfied. This study confirms that indicators which reflected diversification of business and company size latents are good indicators to be used in the structural model. Furthermore, low correlation between latent diversification of business and company size (0.35) reflects that this model achieved discriminant validity (Hair et

al., 2006). Its aim is to ensure that diversification of business and company size were different constructs (Hair et al., 2006). If there was a high correlation between them (r > 0.7), it would mean both of these latent variables belonged to a similar construct. This result was consistent with the result of variance extracted (VE) that diversification of business and company size were two different latent variables as expected by the theory. Thus, the model can be accepted (Hair et al., 2006). This was indicated by variance extracted for diversification of business (0.61) and company size (0.66 ), which were greater than the squared of correlation among two latent variables (r2 = 0.12). This result shows that a latent construct explains its indicators better than it explains another construct. All those were explained in the Table 4.

Table 4Output of CFA for Diversification of Business and Company Size

Latent DimensionsStd.

Loading (SL)

SMC = (SL2)

EV =(1-SMC)

SE C.R p

Diversification of business

HISales_sq -0.69 0.48 0.52 0.02 -9.87 0.00

HI_Assets -0.79 0.62 0.38 0.05 -10.71 0.00

NoSegment_sqrt* 0.85 0.73 0.27

∑ 2.33 1.83 1.17

Construct Reliability 0.82

Variance extracted 0.61

Company size LnSales_sq 0.85 0.72 0.28 0.17 11.07 0.00

LnMVE_sqrt* 0.71 0.51 0.49

LnAssets 0.86 0.74 0.26 0.65 11.06 0.00

∑ 2.42 1.97 1.03

Construct Reliability 0.85

Variance extracted 0.66Note. C.R: Critical ratio; EV: Error variance; p: Probability; SE: Standard error; SL: Standardized loading; SMC: Squared multiple correlations*:Those indicators are fixed parameters which were given value ’1’ (default) by AMOS program (Byrn, 2001). As required by AMOS program, a value “1” on one indicator is given for every latent construct in order for other parameters to be estimated. Therefore, those parameters were not to be estimated as there were no SE, CR, and p values for them.

Moreover, CFA of diversification of business and company size did not only achieve construct validity which would produce a robust result (Hair et al., 2006) but also provided acceptable fit which could be explained by its GOF indices which is represented in Table 5. The χ2/DF ratio or CMIN, CFI, GFI and TLI indicated a better fit since their value could achieve the cut off value (χ2/DF = 2.58 < 3, CFI = 0.98 > 0.90, GFI = 0.98 > 0.90, TLI = 0.96 > 0.90). According to RMSEA, the model is fit since the

value of RMSEA is 0.08. Overall, GOF indices could fulfill the cut off values requirement. Once the measurement model for exogenous latent variables was conducted, overall measurement model was executed (for CFA).

Furthermore, overall measurement model (CFA) for diversification of business, company size and company performance was also executed as showed by Figure 5. This study found that the number of distinct sample moments, parameter and degree of freedom were 45, 26 and 19 (45-

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was


26) respectively. This means that the model was over-identified and could be analyzed.

Table 5.Goodness of Fit Indices of

CFA for Diversification of Business and Company Size

Goodness of Fit Indices Statistic Cut off Value Decision

Chi-Square (χ2)DfProbability (p-Value)RatioGFIAGFICFITLIRMSEA

15.47 6

0.022.580.980.920.980.960.08

Lowest

≥0.05≤3.00≥0.90≥0.90≥0.94≥0.95≤0.08

-Better fitBetter fitBetter fitBetter fitBetter fitBetter fit

Sources: (Byrne, 2001; Ferdinand, 2006; Hair et al., 2006). GFI: Goodness of fit index; AGFI: Adjusted GFI; CFI: Comparative fit index; TLI: Tucker Lewis index; RMSEA: The root mean square error approximation.

The overall measurement model was modified as suggested by modification index and supported by the theory which correlated error between e1 and e5 (LnAssets and HIAssets); e1 and e8 (LnAssets and ROA); e2 and e9 (LnSales and MBVR); e3 and e4 (LnMVE and HISales); e3 and e9 (LnMVE and MBVR). All correlations among the errors were rather low with the highest

value of 0.50 (LnAssets and ROA; LnMVE and MBVR) and the lowest correlation was 0.21 (LnMVE and HISales). When the errors are correlated, chi-square falls at least as much as modification index value. In addition, the objective of modified model is to achieve a lower and an insignificant chi-square which indicates that the model fits the data.

Figure 5

Size

.77

LnAssets

e1

.87

.73

LnSales_sq

e2

.85

.55

LnMVE_sqrt

e3

Diversification

.70

NoSegment_sqrte6

.64

HI_Assetse5

.50

HISales_sqe4

CompanyPerformance

.29

SMEAN(LnROE) e7

.13

SMEAN(ROA_sqrt) e8

.41

MBVR_ln e9

.35

.12

.26

-.50

.50

.30

.46

-.21

.64

.36

.54

-.71

-.80

.83

.74

Standardized estimates Goodness-of- fit indexes:Ratio:2.407; Prob:.001; GFI:.955; CFI:.962; TLI:.927; RMSEA:.082


CFA for Overall Measurement Model

Moreover, on average, the model can fulfill convergent validity which means the indicators can explain the latent variables. According to Anderson and Gerbing (1988) as cited by Ferdinand (2006), Hair et al. (2006), and Tabachnick and Fidell (2007), there are several ways to assess convergent validity such as factor loading, variance extracted, critical ratio, and construct reliability. In terms of factor loadings, Table 6 showed that all the factor loadings are significant at 0.001 level, with loading values ranging from 0.36 to 0.87. According to Tabachnick and Fidell (2007), the factor loadings with a value more than 0.3 showed a convergent validity.

Indicators of diversification of business had factor loadings as follows: Herfindahl index by sales (-0.71), Herfindahl index by assets (-0.80) and the number of business segments (0.83). This indicates that all measures could manifest diversification of business. Although all

are significant but the number of business segments (0.83) represents diversification of business latent better than other indicators. Moreover, company size could be explained by its manifests since the natural log of total assets, the natural log of sales and the natural log of MVE had factor loadings of 0.87, 0.85, and 0.74, respectively. All factor loadings are significant and are more than 0.3, which indicates that convergent validity was achieved. Nevertheless, among the three indicators representing company size, the natural log of total assets is the most important because it has a higher factor loading (0.87). Finally, company performance had factor loadings as follows: 0.64 (MBVR), 0.36 (ROA) and 0.54 (ROE). This means that all measures could manifest company performance, but market-based measure (MBVR) is closely linked to company performance because it has a higher factor loading (0.64). This is a contribution of SEM.

Table 6Output of Overall CFA

Latent DimensionsStd. Loading (SL)

SMC (SL2)EV =(1-SMC)

SE C.R p

Company Performance

MBVR_ln 0.64 0.41 0.59 0.14 3.80 0.00ROA_sq_1 0.36 0.13 0.87 0.02 3.26 0.00ROE_Ln_1* 0.54 0.29 0.71∑ 1.54 0.83 2.17Construct reliability 0.52Variance extracted 0.30

Diversification of business

HISales_sq -0.71 0.50 0.50 0.02 -9.98 0.00HI_Assets -0.80 0.64 0.36 0.05 -10.69 0.00NoSegment_sqrt* 0.83 0.70 0.30∑ 2.34 1.84 1.16Construct reliability 0.82

Variance extracted 0.61

Company size

LnSales_sq 0.85 0.72 0.28 0.02 14.08 0.00

LnMVE_sqrt 0.74 0.55 0.45 0.01 12.28 0.00LnAssets* 0.87 0.76 0.24∑ 2.47

2.03 0.97

Construct reliability 0.86Variance extracted 0.68

C.R: Critical Ratio; EV: Error variance; P: Probability; SE: Standard error*: Those indicators are fixed parameters which were given value ’1’ (default) by AMOS program (Byrn, 2001). As required by AMOS program, a value “1” on one indicator is given for every latent construct in order for otherparameters to be estimated. Therefore, those parameters were not to be estimated as there were no SE, CR, and

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p values for them.

Additionally, the standardized loadings (SL) and critical ratios (C.R were double the standard error) indicated the convergent validity was fulfilled (Anderson and Gerbing (1988) as cited in Ferdinand (2006)); specifically their values were MBVR (SL = 0.64, C.R = 3.80, 2SE = 0.27), ROA (SL = 0.36, C.R = 3.26, 2SE = 0.04), HISales (SL = -0.71, C.R = -9.98, 2SE = 0.04), HIAssets (SL = -0.80, C.R = -10.69, 2SE = 0.10), LnSales (SL = 0.85, C.R = 14.08, 2SE = 0.04), and LnMVE (SL = 0.74, C.R = 12.28, 2SE = 0.02). All figures showed that the latent variables (diversification of business, company size and company performance) could be manifested by their own indicators; hence convergent validity could be fulfilled.

Similarly, the variance extracted and construct reliability of diversification of business and company size achieves the convergent validity because their values were more than 0.5 for variance extracted and 0.7 for construct reliability (Hair et al., 2006). Specifically, diversification of business had variance extracted of 0.61 and construct reliability of 0.82 while company size had variance extracted of 0.68 and construct reliability of 0.86. Company performance had variance extracted of 0.30 and construct reliability of 0.52. This indicated that diversification of business, company size and company performance were reflected well by its own indicators as suggested by the related theory.

The results also show that discriminant validity was established when none of the

correlations among the constructs were more than 0.9 (Hair et al., 2006). The lowest and highest correlations were 0.12 (diversification and company performance) and 0.35 (size and company performance), whereas the correlation between diversification and size was 0.26. Further, the square of correlations among the constructs (0.01 for diversification and company performance, 0.12 for size and company performance and 0.07 for diversification and size) were less than variance extracted for each construct (VE of company performance = 0.30, VE of diversification = 0.61, VE of size = 0.68). It shows that each of the latent constuct explains its indicators better than it explains other constructs. Therefore, this study could fulfill discriminant validity. In brief, when the measurement model could fulfill convergent and discriminant validity, the CFA would have better fit. This means the measurement models fit the data collection in listed companies on the IDX. Table 4 exhibits the output of overall CFA which included standardized factor loadings, construct reliability, variance extracted, SMC, critical ratio, standard error and p value.

Moreover, Table 7 presents that the overall measurement model was a good fit since its GOF could achieve the cut off values (χ2/df ratio = 2.41, GFI = 0.95, AGFI = 0.90, CFI = 0.96 and RMSEA = 0.08). However, chi-square statistics was significant (χ2 = 45.73, df = 19 and p = 0.001) and TLI was slightly below cut off point of 0.95 (0.93).

Table 7Goodness of Fit Indices of Overall CFA

Goodness of Fit Indices Statistic Cut off Value Decision

Chi-Square (χ2)DfProbability(p-Value)RatioGFIAGFICFITLIRMSEA

45.726 190.001

2.410.950.900.960.930.08

Lowest

≥0.05

≤3.00≥0.90≥0.90≥0.94≥0.95≤0.08

-

Better fitBetter fitBetter fitBetter fitGoodBetter fit

Sources: (Byrne, 2001; Ferdinand, 2006; Hair et al., 2006); GFI: Goodness of fit index; AGFI: Adjusted GFI; CFI: Comparative fit index; TLI: Tucker Lewis index; RMSEA: The root mean


square error approximation.

The rejection of a model on the basis of chi-square alone is inappropriate (Bagozzi & Yi, 1988). A significant chi-square might be due to type I error in which there is a rejection of null hypothesis. Chi-square is very sensitive to sample size; therefore, this study used other GOF indices (such as shown in Table 2) to decide whether the model is fit. This was suggested by Tanaka (1993), and Tomarken and Waller (2003). In brief, measurement models in this study were valid and fit.

CONCLUSIONS AND RECOMMENDATIONS

The hypothesized measurement model in this study was accepted which meant that the measurement model was fit with the data collected in listed companies on IDX. All indicators were significant and more than 0.3 which showed that they could represent each their latent construct. The number of business segments is closely linked to diversification of business because it has a higher factor loading while the natural log of total assets has a higher factor loading which shows that it is the most important to represent the company size latent. The market-based measure (MBVR) could represent company performance better than accounting-based measures. This measurement model could achieve convergent and construct validity which would mean that sample could reflect the population. Future research could use more indicators to measure business diversification, company size and company performance.

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