BIOIL SAS

A number of suitability criteria have been used to assess the overall fit of the hypothesised SEM model. suitability measures the extent to which the actual or observed covariance input matrix corresponds with (or departs from) that predicted from the proposed model (Ho, 2006). Goodness-of-fit measures can be classified into three types:

i. absolute fit measures to assess the overall model fit;

ii. incremental fit measures to compare the proposed model to a comparison model; and

iii. Parsimonious fit measures to adjust the measures of finest to compare models with different numbers of coefficients, and determine the fit achieved by each

A. Absolute Fit Measures

Absolute fit indices determine how well a priori model fits the sample data (McDonald & Ho, 2002) and demonstrate which proposed model has the most superior fit. These measures provide the most fundamental indication of how well the proposed theory fits the data. In this category, the model fit guidelines used are the chi-squared test, RMSEA, GFI and AGFI.

The chi-square (χ2

) is considered the most fundamental measure of overall fit (Bollen, 1989). This is a test of whether the matrix of implied variance and covariance (∑) is significantly different to the matrix of empirical sample variance and covariance (S). If the probability (P) is greater than 0.05, this indicates that the discrepancy between ∑ and S is very small, meaning that the actual and predicted input matrices are not statistically different. Although this type of statistical index is the most important one to evaluate model fitness, it has been criticised for being too sensitive to sample size (Fornell & Larcker, 1981; Marsh & Balla, 1994; Hu & Bentler, 1995). Thus, researchers do not solely use the value of chi-square to reject or accept their models, but use in conjunction with other indices to evaluate overall fit.

The second measure of absolute fit indexes used within this study is the Root Mean Square Error of Approximation (RMSEA). This measure assists in correcting the tendency of chi-square to reject specified models. It takes into account error approximation in the population. Holmes-Smith et al. (2006) recommend that RMSEA should be less than 0.05, while Brown and Cuddeck (1992) as reported in Bollen and Long (1993) recommend that a absolute RMSEA value of less than 0.05 indicates a

close fit, and less than 0.08 suggests a reasonable fit. However, it has been found that a value ranging from 0.05 to 0.08 is commonly acceptable (Hair et al., 1995).

The third measure of absolute fitness index used is the Goodness-of-Fit Index (GFI). The Goodness-of-Fit statistic was created by Jöreskog and Sörbom (1981) as an alternative to the Chi-Square test, and calculates the proportion of variance that is accounted for by the estimated population covariance (Tabachnick & Fidell, 2007). The GFI measure indicates the relative amount of variance and covariance together explained by the model (Byrne, 1989). The GFI value is calculated by comparing the discrepancy value for the model under test to the discrepancy value for a saturated version of the model, which is counted as representing a 100% fit or 1.0. However, this measure is not adjusted for degrees of freedom (Hair et al., 1995), ranging from 0 (indicating a poor fit) to 1 (indicating a perfect fit), where a recommended level of acceptance is 0.90 (Kline, 2005; Schumacker & Lomax, 2008; Byrne, 2010).

B. Incremental Fit Measures

The second category of indices includes incremental fit measures. Related to the GFI is the Adjusted Goodness-of-Fit Index (AGFI) which adjusts the GFI based upon degrees of freedom, with more saturated models reducing fit (Tabachnick & Fidell, 2007). Thus, more parsimonious models are preferred, while penalised for complicated models. In addition to this, AGFI tends to increase with sample size. As with the GFI, values for the AGFI also range between 0 and 1, and it is generally accepted that values of 0.80 or greater indicate well-fit models (Chau & Hu, 2001). Given the often

stand-alone index, however given their historical importance, they are often reported in covariance structure analyses (Hooper et al., 2008).

In addition to AGFI, Normed Fit Index (NFI) is one of the most popular incremental measures (Hair et al., 1995; Byrne, 2001). NFI reflects the proportion to which the researchers’ model fits compared to the null model. For example, NFI= 0.50 means the researcher’s model improve fitness by 50%. However, this index does not control the

degrees of freedom (Bollen, 1989). A major drawback to this index is that it is sensitive to sample size, underestimating fitness for samples less than 200 (Mulaik et al., 1989; Bentler, 1990). accordingly, it is not recommended to be solely relied on (Kline, 2005). This problem was rectified by the Non-Normed Fit Index (NNFI), also known as the Tucker-Lewis Index (TLI), which prefers simpler models. In order to overcome NFI’s shortcomings, Bentler (1990) has used it with the Comparative Fit Index (C.F.I.).l The CFI compares the covariance matrix predicted by the model to the observed covariance matrix. However, only NNFI and CFI are reported in this thesis. They ranged from 0 (poor fit) to 1 (perfect fit), having commonly recommended a level of 0.90 or greater (Hair et al., 1995).

C. Parsimony Fitness Measures

According to Hair et al., (1995), the third category of parsimonious fit indices tests the parsimony of the proposed model by evaluating the fitness of the model to the number of estimated coefficient required to achieve the level of fit. In this category, the normed chi-square (χ2/df) - also known as CMIN – is the most popular parsimonious fitness index used to evaluate this model. In this measure, a range of acceptable values for the

χ2

/df ratio have been suggested, ranging from less than 3.0 (Carmines & McIver, 1981). This thesis has used this measure as an indicator of overall fit, in conjunction with other measures, not as a basis for rejecting or accepting the model.

As a summary, in SEM, there are a series of goodness-of-fit indices, which identify whether the model fits the data or not. There are many indices provided by SEM, although there is no agreement among scholars as to which fit indices should be reported. For example Anderson and Gerbing (1988) suggest that researchers might assess how well the specified model accounts for data with one or more overall goodness-of-fit indices. Kline (1998) recommends at least four, such as GFI, NFI or C.F.I., NNFI and SRMR In order to reflect diverse criteria and provide the best overall picture of the model fit, Jaccard and Wan (1996), Bollen and Long (1993), Hair et al. (1995), and Holmes-Smith et al., (2006) recommend the use of at least three fit indices by including one in each category: absolute; incremental; and parsimonious which are discussed below.

This study adopts those measures most commonly used in supply chain and logistics research to evaluate models in which the three categories are reflected. Table 5-2 reports SEM fit indices reported in this study. As outlined in the table, the first category of absolute values includes chi-square (χ2

), GFI, and RMSEA; the second category (incremental) includes AGFI, NFI, CFI, TLI the third category (parsimonious) includes χ2

Table 5-2: Goodness-of-Fit (GOF) Statistics Used in the Thesis

Statistics Fit Criteria Comments

Absolute fit indices

Chi-square (χ2) p>0.05 This measure is sensitive to large

sample sizes

Goodness-of-Fi (GFI) 0.90 or greater

Value close to 0 indicates poor fit, while value close to 1 indicates a perfect fit

Root Mean Square Error of Approximation (RMSEA)

≤0.08 Value up to 1.0 is considered acceptable

Incremental fit Indices

Adjusted Goodness-of-

Fit (AGFI) 0.80 or greater

Value close to 0 indicates a poor fit, while close to 1 indicates a perfect fit Tuker-Lewis Index (TLI)

0.90 or greater Normed Fit Index (NFI)

Comparative Fit Index (CFI)

Parsimonious fit indices

Normed Chi-square (χ2

/ df) 1.0≤ χ

2

/ df ≤5 Lower limit is 1.0, upper limit is 3.0 or as high as 5.0

Source: Adapted from Hair and Black (2006), Chau and Hu (2001), Brown and Cudeck (1993), Bagozzi and Yi (1988), Bentler and Bonnet (1980)