It is unusual to obtain data sets without some missing data (Hair et al. 2006). Missing data occur when a respondent fails to answer one or more questions in a survey. Hair et al.(2006) suggested that missing data will impact on the reduction of the sample size available for analysis if the remedies for missing data are not applied. Moreover, any statistical results based on data with a non-random missing data process could be biased if the missing data led to inaccurate results. In addition, in multivariate analysis, the problem of missing data could be mainly with the saturated model and it may be impractical to fit this model. In particular, it is necessary to find missing data where valid values of one or more variables are not available for analysis.
As this research performed structural equation modelling (SEM), Arbuckle (2005) determines the problem of missing data in SEM using AMOS. With incomplete data AMOS cannot provide fit cannot be computed to the entire saturated model by using fit measures (see Chapter 6). Also, AMOS cannot compute the Modification Indices (M.I.), which help to evaluate various potential modifications in a single analysis and direct suggestions for model modifications (Arbuckle 2005). If there are missing values, an attempt to fit these models
162 requires further extensive computation. The reason is because some missing data value
patterns can make it impossible to fit the saturated model even if it is possible to fit the potential framework.
Tabachnick & Fidell (2001) recommended evaluation of the degree to which there are missing data because missing data usually occur when a respondent fails to answer one or more questions in the survey. There are two actions that can handle the missing data: delete the cases with the consequence of reducing sample size, or by using a remedy. Hair et al. (2006) recommended the way to identify the patterns and relationships of the missing data to maintain as close as possible the original distribution of values. There are four steps to identify missing data and applying remedies: 1) determine the type of missing data; 2)
determine the extent of missing data; 3) diagnosing randomness of missing data; and 4) select the imputation method.
5.3.1.1 Determine the type of missing data
There are two types of missing data: ignorable or not ignorable. Specific remedies for missing data are not needed because the allowances for missing data are inherent in the techniques used (Little & Rubin 2002; Schafer 1997), thus enquiring no remedy (ignorable missing data). However, with the requirement of AMOS, missing data cannot be classified as ignorable as AMOS requires a complete data set. The missing data then cannot be ignored and it is necessary to proceed to the step to determine the extent of missing data. Thus, it is necessary to proceed to the second step to determine the extent of missing data.
5.3.1.2 Determine the Extent of Missing Data
In this step, Hair et al. (2006) suggest that direct means of assessing the extent of missing data are using tabulating: 1) the percentage of variables with missing data for each case; and 2) the
163 number of cases with missing data for each variable. This can be generated by SPSS missing data analysis. In this research, the screening of the data in SPSS indicated that there was no variable that had more than 4% of missing data (see Appendix A7) and since this is less than 5 percent, it can be ignored (Churchill 1995). After using missing data analysis in SPSS (17.0), it was found that the percentage of each variable as missing data was in the range of
0.7% and 3.3% and so can be ignored. Thus, there was no requirement to assess the pattern of missing data (Churchill 1995; Tabachnick & Fidell 2001). Using structural equation
modelling with the AMOS (7.0) application program as required, the missing data cannot be ignored under any circumstance. Nevertheless, to ensure that there is no systematic error (the missing data were randomly distributed) in the responses, the randomness of missing data is required to be assessed (Hair et al. 2006). Thus, it is necessary to go to the next step.
5.3.1.3 Diagnosing Randomness of Missing Data
In diagnosing randomness of missing data, there are 4 techniques utilized in the SPSS
program: 1) Listwise; 2) Pairwise; 3) expectation maximisation (EM); and 4) regression. It is necessary to ensure whether the missing data process shows in a completely random manner. Hair et al. (2006) suggested that even though the sample size is small, it is essential to use a specific statistical program to diagnostic the missing data. In this study, Missing Completely at Random (MCAR), which is sufficiently random to accommodate any type of missing data remedy (Little & Rubin 2002) is appropriate and recommended by Hair et al. (2006).
In this step, Expectation Maximisation (EM) missing data analysis is performed. The EM method is an iterative process to predict the values of the missing variables using all other variables relevant to the construct of interest (Cunningham 2008). The EM analysis estimates missing values by an interactive process which has an “E” step to calculate expected values of parameters and an “M” procedure to calculate maximum likelihood estimates. EM displays
164 means, correlation matrix, and covariance matrix, computed using an EM algorithm. Thus, in this study, Little’s MCAR (Missing Completely At Random) (Little & Rubin 2002) test shows Chi-Square = 1073.33, Degree of Freedom (DF) = 1084, and a significant level (Sig) of 0.58. This indicated that no differences were found between the pattern of missing data on most of variables and the pattern expected for a random missing data process. Thus, it can be concluded that missing data can be classified as MCAR and indicated that the widest range of pot ential remedies can be used.
5.3.1.4 Select the Imputation Method
Due to the requirements of AMOS, the extent of missing data was less than 10%, but this cannot be ignored. In this step, the regression method of imputation is considered to calculate the replacement values based on the rules that the missing data are less than 10 percent
(maximum = 3.3%) and classified as MCAR. When using a regression imputation method with SPSS, the variables that will be used in SEM with AMOS data analysis are complete and free of missing data. This indicates that the data are appropriate and ready to be further investigated.