The Constrictive Definition of Multivariate Analysis - Essay Example

?Multivariate Analysis and Application 0. Introduction and Overview The constrictive definition of multivariate analysis is that by Tabachnick and Fidell (2007). According to Tabachnick and Fidell (2007, p. 2), multivariate statistics consists of studying simultaneously multiple independent and multiple dependent variables. However, many of the books in statistics and research are less restrictive and consider multivariate analysis as those involving multiple independent variables wherein the dependent variable or variables can be only one or many. Hair et al. (1995) is one of the materials with a less restrictive analysis. Hair et al. (1994, p. 2) defined multivariate as analysis of several variables within a relationship or set of relationships. Hair et al. (1995, p. 13) explicit include multiple regression (a regression with one dependent variable and multiple independent variable) as an example of multivariate data analysis. Singh (2007, p. 177) share the same perspective of Hair et al. (1995) on a less restrictive definition of multivariate analysis. We study Kogid et al. (2010) and Shelleman et al. (2004) as illustrations of how multivariate analysis can be applied. 2.0. Kogid et al. (2010) As indicated in the abstract, the objective of the Kogid et al. (2010, p. 123) is to “investigate the factors that stimulate and maintain economic growth.” The factors investigated covered consumption expenditure, government expenditure, export, exchange rate, and foreign investments. The research focused on Malaysia and used data from 1970 to 2007. The specific multivariate statistic technique used by the Kogit et al. (2010) is technique known as “cointegration” and “causality approach”. Cointegration is discussed in Gujarati (2004, p. 822-826). Causality is discussed in Gujarati (2004, p. 696-702). One important test for causality is in Gujarati (2004, p. 696-702). According to Gujarati (2004, p. 822), cointegration means that two or more variables move together and that they have a long-term relationship. The test for cointegration is on the residual of a regression (Gujarati 2004, p. 822). If the regression is stationary or that they do not move randomly then they have a long-term relationship even if we are still unable to define their relationship in a functional form (Gujarati 2004, p. 822). Most tests of causations use tests of correlations. However, other tests go beyond correlation. One of such tests is the Granger causality test. Granger causality test actually test precedence and precedence is taken to be indicative of causality. Unfortunately, Gujarati (2004) does not record a capability of the Granger causality test to cover more than two variables at time (although it can be argued that the Granger causality test has that potential if a composite value covering several variables is constructed). In contrast, the Wald test as performed by Kogit et al. (2010) implies a capability of the Wald test to investigate relations of causation that involve more than two variables. Extensive search on the Wald Test conducted by this author in the books indicates that the Wald Test for causation is not yet discussed in many of the books. However, the works of Atinay and Karagol (2005), Burda (2001), No and Olatubi (2004), and Zarra and Zarea (2007) have good discussions on the Wald Test. The results of the study of Kogit et al. (2010) indicate that long-run cointegration and short-run causal relationship exists between the investigated factors and economic growth. The fundamental and important finding is all the factors investigated when combined can in their combination cause economic growth in the short-run. However, on their own, the individual regressions indicate that only consumption expenditure and export can on its own cause economic growth in the short-run. For brevity, we reproduce only the key test which is the causality test. The causality test is captured by Table 1. Table 1. Multivariate and Bivariate Causality Tests Using the Error Correction Model (ECM) Source: Table 3 of Kogit et al. (2010, p. 134) Kogit et al. (2010, p. 123) believe that their data and statistical results support the conclusion that expenditure and export play are important determinants of economic growth but the rest of the investigated factors play a catalyst and complementary role in the economic growth of Malaysia. The magnitudes of the Wald Test statistic are in the third column of Table 1. However, this is not the magnitude of the causation but the magnitude only of the Weld Test statistic. There are no magnitude values for causation. The null hypothesis is that the variable or variables assumed as independent are not the cause of the variable assumed as dependent. The alternative hypothesis is that the variable or variables assumed as independent causes the variable assumed as dependent. We construct the null hypotheses indicated by Table 1 in Table 2. Table 2. Null Hypothesis Represented in Table 1 Notation in Table 1 Null Hypothesis Represented by the Notation All variables covered does not cause the logarithm of the gross domestic product The logarithm of consumer expenditure does not cause the logarithm of the gross domestic product The logarithm of government expenditure does not cause the logarithm of the gross domestic product The logarithm of export does not cause the logarithm of the gross domestic product The logarithm of exchange rate does not cause the logarithm of gross domestic product The logarithm of foreign direct investments does not cause the logarithm of the gross domestic product All logarithm values are interpreted as growth. Thus, for example, the “logarithm of the gross domestic product” is interpreted as “the growth of the gross domestic product or economic growth”. The “**” and “***” mean that the null hypothesis is rejected at the .05 and .01 levels, respectively. Following the procedure adopted by Kogit et al. (2010), the null hypothesis is rejected at the .05 level. The null hypothesis is rejected at the .01 level. Finally, the null hypothesis is rejected at the .05 level. The immediate limitation, of course, is the rejection of null hypothesis may be made when, in fact, the null hypothesis is true. Another limitation is built in the nature of the Wald Test: most likely, just like in the other tests of causation, precedence is considered evidence of causation when in fact it is not. 3.0. Shelleman et al. (2004) Figure 1. Determinants of Treated but with Uncontrolled Hypertension Source: Figure 1b, Shelleman et al. (2004, p. 321) The overall objective of Shelleman et al. (2004, p. 317) was to “determine the prevalence, treatment, and control of hypertension, and the determinants of undertreatment in the Dutch population.” It was in the specific the assessment of the determinants of undertreatment of hypertension in the Dutch population where a multivariate analysis was used. Shelleman et al. (2004) used multivariate logistic regression in the multivariate analysis of the determinants of treatment and under-treatment. Multivariate logistic regression was employed to analyze the relationship between demographic variables, cardiovascular risk factors, medication used on one hand, and the treatment and control of hypertension as dependent variables (Schelleman 2004, p. 319). The multivariate regression results for treatment but with uncontrolled hypertension are reported in Figure 1 that comes from Figure 1b of Shelleman et al. (2004, p. 321). Based on the results those who use cholesterol-lower medication has been significantly associated with the likelihood of uncontrolled hypertension based on the criterion odds ratio 1 (Shelleman et al. 2004, p. 320). Figure 2. Determinants of Under-treament Source: Figure 1a, Shelleman et al. (2004, p. 321) The values of Figure 1 and 2 and their interpretation are conducted consistent with the prescribed interpretation of Moore and McCabe (2005, p. 16-2 to 16-4). According to Moor and McCabe (2005, p. 16-2 and 16-3), the odds ratio is where the numerator pertains to the probability of the first event and the denominator pertains to the probability of the second event. In Figure 1, the numerator is “less likely to be uncontrolled” and the denominator is “more likely to be uncontrolled” In figure 2, the numerator is “less likely to be untreated” while the denominator is “more likely to be untreated”. The values represented in Figures 1 and 2 represent the coefficient of the independent variable or the betas or ?s in the regression equation in (Moor and McCabe 2005, p. 16-4): . Of course, this is simple regression but the interpretation is the similar as indicated in Gujarati (2004, p. 592) in the regression of . Thus, the magnitude of the coefficient must be understood as its contribution to. The author of Shelleman et al. (2004) did not report statistical significance, indicating that they were not concerned on the generalizability of their results and amounted to an implicit acknowledgement of the limitation of their study. 4.0. Conclusion In this work, we have illustrated that multivariate analysis can do more than univariate analysis. As shown by our illustrative examples, multivariate analysis can do more what univariate or bivariate analysis cannot do. In particular, multivariate analysis and statistics can do the following: analyze multiple variables simultaneously control the effects of variables; assess the joint effect of variables on another variables isolate the effects of one variable by isolating the effects of other variables, and it is able to conduct test of causality involving several variables investigate if several variables can jointly cause or affect another variable. Reference Atinay, G. and Karagol, E., 2005. Electricity consumption and economic growth: Evidence from Turkey. Energy Economics 26, 849-856. Burda, M., 2001. Testing for causality with Wald Tests under nonregular conditions. A Ph. D. Dissertation. University of Berlin. Gujarati, D., 2004. Econometrics. 4th Ed. McGraw-Hill Companies. Hair, J., Anderson, R., Tatham, R., and Black, W., 1995. Multivariate data analysis with readings. 4th Ed. London: Prentice-Hall. Kogid, M., Mulok, D., Beatrice, L., and Manur, K., 2010. Determinants of economic growth in multivariate contegration and causality analysis. European Journal of Economics, Finance and Administrative Sciences, Issue 24, 123-137. Moore, D. and McCabe, G., 2005. Introduction to the practice of statistics. 5th Ed. New York: W.H. Freeman and Company. No, S. and Olatubi, W., 2004. Do Granger-causality test really confine time series forecasting models? The case of US oil prices. Available from: www.sbaer.uca (Accessed 23 April 2011). Schelleman, H., Klungel, OH, Kromhout, D., Boer, A., Stricker, BHCh, and Verschuren, WMM. 2004. Prevalence and determinants of undertreatment of hypertension in the Netherlands. Journal of Human Hypertension, 18, 317-324. Singh, K., 2007. Quantitative social research methods. Los Angeles and London: Sage Publications. Tabachnick, B. and Fidell, L., 2007. Using multivariate statistics. Boston and London: Pearson Education, Inc. Zarra, M. and Zarea, R., 2007. Investigating the causality Granger relationship between the rates of interest and inflation in Iran. Journal of Social Science, 3 (4), 237-244. Annex 1: Abstract of Kogid et al. (2010) Annex 2: Abstract of Shelleman et al. (2004) Read More