Structural Equation Modeling in Management Research: Twenty-Year Veterans and Federal (Research Paper Sample)

Structural Equation Modeling in Management Research: Twenty-Year Veterans and Federal Employment
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Statement of Hypothesis
This research is based on the struggles regarding employment of the retired twenty-year Veteran by the US federal government. It is based on the thesis statements as follows:
The number of twenty year old veterans employed by the US government increased constantly from the year 2009 to 2012.
The average numbers for all the categories increased constantly from 2009 to 2012.
The total number of retired veteran in the different sectors was increasing steadily among all the categories and sectors for all the four years.
At the end of the analysis, there will be a test on all the hypotheses to ascertain whether they are valid or not. Using SPSS, the tests will be run on various data samples to ascertain the level of significance of various variables using multivariate techniques. Ultimately, the tests of the hypotheses will be able to create the decision rules and the actual decisions as they are guided by the data samples. From the decisions, the research process will be able to make an evaluation of the reliability and accuracy of the results by eliminating the abnormality that arises from the limitation of the analysis.
Justification for Using SPSS
SPSS (Statistical Package for Social Sciences) is the most appropriate statistical software for this analysis since it is able to perform various options of analysis compared to STATA and other forms of software. It is very quick in producing output results, and it is easy to use in relation to data editing.
Naming the Variables
The analysis is based on the variables relating to the various categories and for the range of years within the study period. The research variables are divided into two; dependent variables and independent variables.
Dependent variables
Number of Veteran Males (VM)
Number of Veteran Females (VF)
Number of Non Veteran Males (NVM)
Number of Non Veteran Females (NVF)
Number of Retired Veterans (RV)
A sample data set for the variables is shown below:


Figure 1: Sample Raw Data in SPSS Editor
Independent Variables
The only independent variable for this Structural Equation Modeling is the year, whose values range from 2009 to 2012. In other data sets, the independent variables are the sectors under which the retired veterans are employed in the US Federal government. An example of the presentation of the retired veterans by the sectors is shown below:
CategoryFederal StateLocalTotalAverageVM 19014721170.33333VF 127872891297NVM 98216225539179.6667NVF 877093121108369.3333RV 105165462732244Table 1: Categories of Retired Veteran and sectors of Government


Figure 2: Various Sectors of US Government.
Test of Data Samples
The test for the data samples is meant to prove the validity of the hypotheses. The research thus uses a number of relevant data sets as follows:


Figure 3: Sample Data set
YEARVMVFNVMNVFRVAverage2009*14436636662188625702010*14862064586389972742.42011*1524865486489409834672012*16757668767581282759.4Table 2: Sample Data set
Charts and graphs in testing hypothesis
The test results show the corresponding average number of veteran soldiers employed in the different years that the study is concerned with. The graph below is to show the behavior of the numbers employed in different years from 2009 to 2012.
S NoYEARTotal1Y2009128502Y2010137123Y2011173354Y201213797Table 3: Total number employed in the four years


Figure 4: Total Number Employed .
The behavior of these variables shows that there is a constant rise from 2009 to 2011. This proves the first hypothesis to be valid. For the second hypothesis uses average as the measure of trend. Practically, even though the average numbers increase up to 2011 and then falls in 2012, the linear average line is a steady positive gradient line. The average line is a curved line of equation R2 = 0.176 while the linear average line has an equation y = 129.2x + 2561.The availability of co linearity between the two variables shows that the second hypothesis is valid.
CategoryFederalStateLocalTotalAverage20091443663666218862010148620645863899720111524865486489409820121675766876758128Average =average(ABOVE) 152.75 =average(ABOVE) 190.25 =average(ABOVE) 6514.75 =average(ABOVE) 6463.5Table 4: Raw Sample Data for Sectors2009
CategoryFederalStateLocalTotalAverage20091443663666218862010148620645863899720111524865486489409820121675766876758128Average =average(ABOVE) 152.75 =average(ABOVE) 190.25 =average(ABOVE) 6514.75 =average(ABOVE) 6463.5Table 5: Raw Sample Data for Sectors2010
CategoryFederalStateLocalTotalAverageVM 16012417658.66667VF 107655672224NVM 62200326588.33333NVF 6570923797265.6667RV 133126344603201Table 6: Raw Sample Data for Sectors2011
CategoryFederalStateLocalTotalAverage2009156415649759056201014841402836091002011160544820346530020121776060457283140Average =average(ABOVE) 160.25 =average(ABOVE) 49 =average(ABOVE) 5135.5 =average(ABOVE) 5486.75Table 7: Raw Sample Data for Sectors2012


Figure 5: Average Number of Employed Veterans
For the test to be successful for hypothesis 3, the research uses the data set below:
YearFederalStateLocalTotal2009141142920101910938201110462020123249Average =average(ABOVE) 11.5 =SUM(ABOVE) 27 =SUM(ABOVE) 23Table 8: Number employed in each sector
The table 4 above shows that the number of the retired veteran soldiers began to rise from 2009 to 2010. However, immediately after that, the numbers continued to reduce constantly up to 2012. According to this evidence, the third hypothesis is not valid.


Figure 6: Numbers employed in each sector


Figure 7: Total number of veterans employed
The trend of the numbers employedper sector appear to be reducing steadily from 2010 after increasing once between 2009 and 2010. This implies that the third hypothesis has failed the test.
SPSS Analysis
In the SPSS analysis, we use various methods to perform computations of the structured equation models. The methods used include the central tendencies, multivariate analysis, kurtosis and scenes.
Central Tendencies and dispersal
In central Tendencies, the analysis is purely based on the measure of mean, mode and the median values of the variables. In the measures of dispersal, the analysis considers measures such as the standard deviation and the standard error (Tsang, 2002). It also check extreme values (outliers) and missing values or values out of range to determine the existence of or the absence of error. The SPSS output below shows the measures in form of a report.


Figure 8: Summary of the Sectors and categories
The report below summarizes all the means and the standard deviations for all the sectors year by year from 2009 to 2012. The greatest effect is experienced in 2010 as shown by the mean, while the standard deviation is greatest in the case of Federal government, followed by the state and eventually by the Local government.


Figure 9: Report on Mean and Standard deviations
The summary for univariate statistics appears in the figure below,


Figure 10: Confirmation of Cases out of Range
Use of Multivariate Techniques
In this analysis, the research combines the various variables by using methods like mixed model and general linear Models.


Figure 11: General Linear Model


Figure 12: Generalized Linear Model Analysis


Figure 13: Information on Continuous Variable Analysis


Figure 14: Comparing the fitness of the models


Figure 15: Estimate of Parameters and standard errors
The Models in marginal means show covariates of fixed nature. The standard error for all the variable computations is 1 as shown in the figure below:


Figure 16: Estimate of marginal Means


Figure 17: Correlation Analysis Models
From the Pearson’s correlation analysis, the coefficient of correlation is:
State to Federal = 0.784
Federal to Local= 0.798
State to local = 0.999


Figure 18: Pearson Correlation analysis for all sectors


Figure 19: Spearman’s and Kendall’s Correlation for the sectors


Figure 20: Correlation Models for the subject effects
Concerns or Abnormality
In the analysis, there are figures that are very different from the inherent assumptions made by the hypothesis. A good example is in the Wald Chi Square from the Omnibus Test. It shows the number of 1449602.383 related to the Veteran females, which is a derivative of sum of squares. Secondly, the intercepts are showing exponential values which apparently are out of range. This might have had an adverse effect on the results and thus influenced the test for hypothesis. The other face of abnormality is the trend where all other datasets are expected to indicate a growing trend in the number of twenty year old veterans who the US government employs. The test produces an exception where the dataset for categories and sectors reduces constantly from 2008 onwards contrary to the hypothesis. The numbers of sets of fit indices that are produced determine the interpretation of the measurement of the model. It can reflect how well the model represents group data for the multiple variable sets of data. In the omnibus test and the goodness (fit) test, the indexes for the fit are favorable, implying that the data items were interpreted using the very constructs in every data sample. The tes...