Twenty-Year Veterans and Federal Employment - Report Example

Structural Equation Modeling in Management Research: Twenty-Year Veterans and Federal Employment ment 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: 1. The number of twenty year old veterans employed by the US government increased constantly from the year 2009 to 2012. 2. The average numbers for all the categories increased constantly from 2009 to 2012. 3. The total number of retired veterans 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: Category Federal State Local Total Average VM 190 14 7 211 70.33333 VF 12 7 872 891 297 NVM 98 216 225 539 179.6667 NVF 87 709 312 1108 369.3333 RV 105 165 462 732 244 Table 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 YEAR VM VF NVM NVF RV Average 2009* 144 36 6366 6218 86 2570 2010* 148 620 6458 6389 97 2742.4 2011* 152 48 6548 6489 4098 3467 2012* 167 57 6687 6758 128 2759.4 Table 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 No YEAR Total 1 Y2009 12850 2 Y2010 13712 3 Y2011 17335 4 Y2012 13797 Table 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, it 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. Category Federal State Local Total Average 2009 144 36 6366 6218 86 2010 148 620 6458 6389 97 2011 152 48 6548 6489 4098 2012 167 57 6687 6758 128 Average 152.75 190.25 6514.75 6463.5 Table 4: Raw Sample Data for Sectors2009 Category Federal State Local Total Average 2009 144 36 6366 6218 86 2010 148 620 6458 6389 97 2011 152 48 6548 6489 4098 2012 167 57 6687 6758 128 Average 152.75 190.25 6514.75 6463.5 Table 5: Raw Sample Data for Sectors2010 Category Federal State Local Total Average VM 160 12 4 176 58.66667 VF 10 7 655 672 224 NVM 62 200 3 265 88.33333 NVF 65 709 23 797 265.6667 RV 133 126 344 603 201 Table 6: Raw Sample Data for Sectors2011 Category Federal State Local Total Average 2009 156 41 5649 7590 56 2010 148 41 4028 3609 100 2011 160 54 4820 3465 300 2012 177 60 6045 7283 140 Average 160.25 49 5135.5 5486.75 Table 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: Year Federal State Local Total 2009 14 11 4 29 2010 19 10 9 38 2011 10 4 6 20 2012 3 2 4 9 Average 11.5 27 23 Table 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 employed per 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 checks 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 test only compared the fitted model against the intercept only model. Level of Significance The analysis produces test results for the data sets as evidence that guides the decision rules. This is because every single decision must be a derivative of a decision rule which in turn, must be guided by the data results. Since the fit test indices are unfavorable, Bollen (1989) suggests that it is unsafe to conclude that the same construct was used to interpret the items in both groups (Wall & Amemiya, 2001). The invariance in the hypothesis test was supported; therefore, the conclusion is that all the three hypotheses of differences in structural parameters can be tested across the different categories of retired veterans using the present data sets. Of course, the evidence indicates random variables named in this study and the indicators are well connected in similar ways in both of the two groups. Decision Rules Actual Decisions guided by data The decisions to be made on this analysis must be guided by a set of rules. These rules are a set of criteria based on the nature of the data analysis results. The rules are “if ... then” conditions upon the determination of the status of the hypotheses. For example in this case, the first hypothesis can derive a decision rule as follows: If the number of a certain category employed in the entire period is less than 50, then more of the category should be employed in various sectors. With this rule, the sample data set in table 6 will support decisions that more of Non Veteran Males be employed in the Local government, Veteran Males in the Local sector and the state government. The other decision will be to increase the non veteran females in the Local government sector and veteran females in the Federal government sector. The decision will thus generate a different table as shown below. Category Federal State Local Total Average VM 160 72 84 176 58.66667 VF 70 77 655 672 224 NVM 62 200 63 265 88.33333 NVF 65 709 93 797 265.6667 RV 133 126 344 603 201 Table 9: Increased numbers after Decision Another possible decision rule would be that if the average number of veteran employees exceeds 2000, then it has to be brought down to about 200. This will mean that the researcher reduces each individual category to arrive at that average. Taking table 4 as a sample data set, the row for Local government will have to be reduced when the following year comes. Category Federal State Local Total Average 2009 144 36 6366 6218 86 2010 148 620 6458 6389 97 2011 152 48 6548 6489 4098 2012 167 57 6687 6758 128 Average 152.75 190.25 6514.75 6463.5 The decision to be made upon the realization of the configuration invariance must consider the magnitude of the problem being in the abnormal group (Woehr, Sheehan & Bennett, 2005). For example, in the classification of the twenty year old veterans employed by the US government in form of the government sectors create a different list of parameters from that of classification of the veterans in their different variable categories such as female and male. In this study, the variation between the numbers of the various categories creates the need for further diagnosis since the data is problematic (Arminger & Muthén, 1998). The research thus assumes that from a theoretical point of view, in which the hypothetical tests for the group makes wide variances, the test can move on without any mediator variable. All the latent variables are invariantly configurable; hence, the ability to test the hypotheses of the group variation rises (Cheung & Au, 2005). The correlation analysis for all the veteran soldiers groups produces positive coefficients; hence all the groups have configurable invariance. Discussion of results in relation to hypothesis Following the implications for the testing of the three hypotheses, the results are reliant on the level of the invariance. From the results, the variance is relatively low, therefore the research can move on with the tests to confirm the theoretical pattern of increase or decrease in the number of twenty year old veterans employed by the US government. The difference between the three hypotheses is only caused by one, the third hypothesis which is inversely positioned in relation to the first two. The invariance of between the three hypotheses can be corrected by changing the numbers for the subsequent year, which is 2013 such that every sector of the US government can be having incremental orders of numbers employed. If this happens then the hypothesis testing will reveal uniform outcomes for the three hypothetical statements (Sobel, 1996). As it is, the research can rely on the first two hypotheses which have proved to be positive as the hypothesis with the strongest grounds. Incidentally, none of the hypotheses require a combination of multiple variables between two or more groups; hence, there is no need for the researcher to conduct another process of additional data collection. Reliability and Validity of results The assurance of reliability of the results is based on the fact that the data source is the US Census records. This means that the data is accurate, added to the fact that the data file is of a protected format, which makes the data safe from manipulation and possible alteration. It is also valid because the information presented is consistent with the period covered. The figures presented are realistic and whole numbers and the intercept points are consistent across all the groups. The variance between the group data values shows that they are of a uniform spread. In other words, the outliers are kept at minimal levels (Messick, 1995). The results are also accurate, after computation and analysis have been done in SPSS which gives detailed accurate results. The measures of central tendencies and the use of aggregations were found to be more accurate than the use of individual numbers from the raw data samples. Again, the fit (goodness) test revealed a positive indicator of reliability of the results since its strategy was to use small samples to avoid ambiguity. Limitations of the Analysis The analysis has a few limitations in the measure of the overall fit (goodness) of the multiple indicators. There is no single model to connect the latent variable to their indicators. Upon a critical evaluation of the measurement of the model before conducting the analysis with a purpose of testing link between the variables, there is a possibility that the multiple indicator and the latent variable in the model are not of a uniform link as shown in a measurement model (Ployhart & Oswald, 2004). In the case of a model with poor relationship between the latent variables and their relevant indicators, the research is at a risk of making conclusion on hypothesis that have not been exhaustively analyzed. This is a serious risk considering that the relations between the latent variables are vital for the theoretical observations. The overall indices of fitness and goodness combine the information about the measures of structural models into an aggregate value (Brown, 1997). Another limitation is the use of a single statistical tool to conduct the analysis, which can lead to the desire to perform parallel tests using other tools to confirm the consistency of the outcomes. The risk of relying on one system is that the coding of the data analysis tool might have been erroneous, leading to wrong outcomes. References Arminger, G., & Muthén, B.O. (1998). A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the Metropolis-Hastings algorithm. Psychometrika, 254. Bollen, K.A. (1989). Structural equation models with latent variables. New York: John Wiley and Sons. Brown, R.L. (1997). Assessing specific mediational effects in complex theoretical models. Structural Equation Modeling, 12–16. Cheung, M.W.L., & Au, K. (2005). Applications of multilevel structural equation modeling to cross-cultural research. Structural Equation Modeling, 198. Messick, S. (1995). Standards of validity and the validity of standards in performance assessment. Educational Measurement: Issues and Practice, 19-20. Ployhart, R.E., & Oswald, F.L. (2004). Applications of mean and covariance structure analysis: Integrating correlational and experimental approaches. Organizational Research Methods, 10-12. Sobel, M.E. (1996). An introduction to causal inference. Sociological Methods & Research, 27, 35. Tsang, E.W.K. (2002). Acquiring knowledge by foreign partners from international joint ventures in a transition economy: Learning-by-doing and learning myopia. Strategic Management Journal, 24. Wall, M.M., & Amemiya, Y. (2001). Generalized appended product indicator procedure for nonlinear structural equation analysis. Journal of Educational and Behavioral Statistics, 28–32. Woehr, D.J., Sheehan, M.K., & Bennett, W. (2005). Assessing measurement equivalence across ratings sources: A multitrait–multirater approach. Journal of Applied Psychology, 97. Read More