LOS EXÁMENES COMO PROBLEMA

In SEM, the estimations of the population parameters should be adopted (Tachnick and Fidell 2007). The aim is to minimise the variation between the observed and estimated population covariance matrices. According to Tachnick and Fidell (2007). A number of estimation techniques are available, such as the Maximum likelihood (ML), Generalised Least Square (GLS), Weighted Least Square (WLS), and Unweighted Least Square (ULS) (Byrne, 2009; Tabachnick and Fidell, 2007; Hair et al., 2010). Tabachnick and Fidell (2007) argue that the right estimation technique and the test statistic is essential to consider their performance according to sample size. The default and most frequently used estimation method in AMOS is Maximum Likelihood (Tachnick and Fidell, 2007;

Byrne, 2009). Maximum Likelihood (ML) estimation performs well with a sample size above 500. ML has the advantage that it performs well, even when dealing with data where its normality assumption is violated (Tabachnick and Fidell, 2007). Based on the large sample size requirement for this study (>500) the application of ML estimation technique is statistical, logical and practical to provide appropriate and reliable results (Tabachnick and Fidell, 2007; Hair et al., 2010). ML estimation technique is used by academics during application of SEM to assess acculturation and consumer behaviour (Acker and Vanbeselaere, 2011; Josiassen, 2011).

The fitness of a structural model can be processed by the goodness-of-fit (GOF) indices (Hair et al., 2010). The GOF reveals that if the model misfits, modifications can be made based on modification indexes and theoretical evidences in order to improve the SEM fit model. The GOF compares the theory (estimated covariance matrix) to reality (observed covariance matrix), which indicates how well the specified model fits. This will increase the accuracy of testing the hypotheses and develop an acceptable Immigrants’

consumer acculturation model.

A key consideration for construct validity and reliability is to analyse how all of the individual constructs will come together to form an overall measurement model. One key issue is the establishment of “unidimensional” measures i.e. that a set of measured indicator variables can be explained by only one construct (Hair et al., 2010).

Unidimensional measures make the model more accurate and are an important aspect of scale validity (Hair et al., 2010). Researchers have argued that marketing contributions have overlooked the need to establish whether a scale is unidimensional or not (Gerbing and Anderson, 1988; Jaworski and Kohli, 1993). In this study, unidimensionality tests of each scale were taken before evaluating the structural model as a whole to give an indication of the overall quality of the measures. The overall fit of

the confirmatory factor model, when each factor is hypothesised to be represented by only one factor, “provides the necessary and sufficient information to estimate whether the assumption of construct unidimensionality has been met” (Steenkamp and van Trijp, 1991, p.287). This study takes the guidelines of unidimensional measurement of indicator variables representing only one construct. Byrne (2009) recommends to test unidimensionality with each latent variable independently.

The chi-square is the index of fit for testing unidimensionality as a measure of exact fit (Hair et al., 2010). However, the chi-square rejects the fit of a model as the number of cases increases (Kline, 2011). There are a number of Goodness-of-fit (GOF) measures that can be used to assess a structural model. The of-fit indices, Goodness-of-fit (GFI) and Adjusted Goodness-Goodness-of-fit (AGFI), are popular for unidimensional constructs. One limitation of GFI is that the expected values vary with sample size (Fan, Thompson and Wang, 1999; Kline, 2011). Other fit indices have been developed which decrease the use of GFI (Hair et al., 2010). According to Wheaton (1987) the GFI and AGFI may not be as informative as chi-square test statistics and Root Mean Square Error of Approximation (RMSEA). The chi-square is expected to be a non-significant statistical measure to indicate that no significant difference between sample covariance matrix and the estimated covariance is evidenced (Tabachnick and Fidell, 2007).

Therefore, a good fit can be indicated by a non-significant chi-square statistic. However, chi-square values are affected by sample size and should not be solely used for goodness-of-fit (Hair et al., 2010). Models with large samples often result in the fit statistic to be significant (Jöreskog and Sörbom, 1993). Therefore the /df is used instead. RMSEA is widely used with large samples or large numbers of observed variables (Hair et al., 2010). RMSEA is best suited for large sample size, e.g. sample size larger than 500 respondents (Hair et al., 2010). Kline (2011) and Byrne (2001) recommend to assess a model based on Comparative Fit Index (CFI) and RMSEA. CFI is the most widely used index (Hair et al., 2010).

Several fit indices have been developed to assess a good fit (Tabachnick and Fidell, 2007). It is argued that not all model-fit criteria can meet all goodness-of-fit indices (Schumacher and Lomax, 1996). For example, Kenn and Mccoach (2003) indicated that Tucker-Lewis Index (TLI) and CFI both decline as more variables are added. These authors recommend that a majority of fit indices indicate an acceptable model, in line with Kline (2011). More complex models with larger samples should not be held to strict standards (Hair et al., 2010). If the fit indices are acceptable, then the researcher can proceed with SEM, indicating validity and suggesting that the theoretical model is supported by the data.

The use of three or four fit indices is recommended (Garson, 2008; Hair et al., 2010). In marketing, the normed (CMIN/DF or /df) index together with the CFI, TLI and RMSEA are most commonly used (Cleveland et al., 2011; Josiassen, 2011). The sample size in this study of 530 indicates that the chi-square will probably be significant, thus /df is used instead. The GFI and AGFI indices may be affected by the large sample size and therefore can be applied to lower values than the recommended threshold (Hair et al., 2010).

The four fit indices CMIN/DF, CFI, TLI, RMSEA as guided by marketing literature and recommend by the above researchers to examine the goodness-of-fit of the measurement model are adopted in this study. Josiassen (2011) for example, assessed the Goodness-of-fit of his measurement model acculturation effects on ethnic consumers by utilizing CMIN/DF, CFI and RMSEA model fit statistics. Similarly, Richard and Tofolli (2009) have also applied the same statistics in their assessment of language influence and Cleveland et al. (2011) in their assessment of identity impact on consumer behaviour. The chosen indices follow guidance provided by Hair et al. (2010). The multiple model fit indices include both an absolute as well as incremental model fit, which contributes to the evidence of adequate information to estimate the research measurement model. The fit indices used as guidelines in this study are illustrated in Table 7.

Table 7. Fit Indices in this Study

Measurement Model Reference

CMIN/DF

< 0.5 Tabachnick and Fidell, 2007

< 2 and < 3 Hair et al., 2010

< 2 Kline, 2011

CFI

0.9 Schumacker and Lomax, 2004

> 0.90 Hair et al., 2010

> 0.95 Kline, 2011

TLI

0.9 Schumacker and Lomax, 2004

< 0.90 Hair et al., 2010

< 0.95 Bentler and Hu (1999)

RMSEA

Hair et al., 2010

< 0.08 Kline, 2011

< 0.06 Hu and Bentler, 1999

< 0.05 Schumacker and Lomax, 2004