THE INVESTIGATION OF SUICIDE USING SAS" SOFTWARE PROCEDURES: A SAS" / ETS APPROACH Seid M. Zekavat, Loyola Marymount University INTRODUCTION A careful look at the suicide data suggests a possible link between economic conditions and the suicide trend and patterns. This study intends to provide an answer to the question: Do such aggregate factors as GNP, Unemployment, the Rate of Inflation, have any direct or indirect bearing on the rate of suicide? DATA The suicide data for the period 1930 to 1984 are used as dependent variables. The data are broken into four groups: white male, white female, non-white male and non-white female. Each of these groups is further divided into eight age categories: ages 5 to 14, 15 to 25,..., 5 to 84. The rates are expressed in mortalities per 100,000 population. The independent variables include GNP, Inflation, Unemployment, the Dow Jones average and a dummy variable to represent War. The data for these independent variables correspond to the time period 1930 to 1984. Inflation is expressed as the annual rate of change of the Consumer's Price Index. The Dow Jones figures are usual averages. For the war, figure 1 is used when the U.S. was engaged in war and figure 0 is used when the country enjoyed peace. SAS ECONOMETRIC MODEL A complete first-degree multiple regression model is employed to investigate the relationship of the suicide rate to the economic factors. A qualitative variable war/peace and the Dow Jones are also incorporated into this model. GNP in the model is lagged on the assumption that it would take one to two years span before the impact of low or high levels of aggregate national income is felt by individual income recipient. Rate of Unemployment, however is not lagged. It is quite conceivable that mental depression due to the loss of a job is immediate and would reach a high level especially when the unemployed has little or no hope of regaining his or her employment. To check the probable exaggeration of the impact of the dependent variables, tests of multicollinearity and autocorrelation are conducted using procedures described in manual SAS REGRESSION. The SAS econometric model employed in this study is as follows: suicide Rate 8, + 8, GNP + 8 2 GNPl + 8 3 GNP2 + B4 UNEMP + B5 INF + 56 DOW + 8 WAR + ui where: GNP, GNP1, GNP2: GNP and one and two year lags UNEMP Unemployment Rate in the united states INF Rate of Inflation, cpr 1 during War Years WAR 0 during non-war years DOW Rate of growth of Dow Jones Industrial average 1103
~HE RESUL~S OF ~HE INVES~IGA~ION Total suicides: Analysis of Variance Square F Value 5 129.80589 22.58839 152.39429 18.5430 0.4059 39.405 Oep 0.68600 11.9285 5.508 0.8518 0.8302 variable Parameter standard T for HO: Estimate Parameter=O Prob > IT: INTERCEP GNP GNP1 GNP2 UNEMP INF DOW WAR 1 9.06995 0.3603856 25.16 1 0.002994 0.00254332 1.1 1-0.001266 0.00395900-0.320 1-0.002060 0.00296436-0.695 1 0.303115 0.02265264 13.381 1 0.038443 0.0301459 1.25 1 0.000400 0.0005095 0.8 1 0.343613 0.23622349 1.4 0.2449 0.505 0.4904 0.2084 0.4350 0.1523 Durbin-watson D 0.863 (For Number of Obs.) 56 1st Order Autocorrelation 0.504 SAS Results accordinq to SEX and RACE: White Male: Analysis of Variance Square F Value 38.4931 63.622 450.964.35419 41.852 1. 32263 Dep 1.15006 19.5910 5.8031 0.8592 0.838 Variable INTERCEP GNP GNP1 GNP2 UNEMP INF DOW WAR Parameter Standard T for HO: Estimate Parameter=O 1 15.844 0.60416563 26.128 1 0.001599 0.00426381 0.35 1-0.002385 0.0066316-0.359 1 0.001654 0.00496968 0.333 1 0.46290 0.039658 12.189 1 0.003841 0.05053865 0.06 1-0.001046 0.0008515-1. 229 1 0.200268 0.396022 0.506 Prob > 0.093 0.210 0.40 0.939 0.2252 0.6154 11'1 Durbin-Watson 0 0.954 (For Number of Obs.) 56 1st Order Autocorrelation 0.440 1104
White Female: Analysis of Variance Square F Value 29.5336 15.24092 44.81429 4.224 0.3152 13.306 Dep 0.56349 6.22143 9.0522 ParameterStandardT for HO: VariableEstimatearameter=OProb > :T: INTERCEPt 13.995940.2960205613.498 GNP 10.003584 0.00208912 1.15 0.092 GNP1 1 0.000031025 0.00325198 0.010 GNP2 1-0.008 0.0024349-1. 966 UNEMP 1 0.162 0.0186023 8.988 INF 1 0.06880 0.0246222 3.105 DOW 1 0.001620 0.0004124 3.882 WAR 1 0.60562 0.1940365 3.122 0.6599 0.6103 0.9924 0.01 0.0032 0.0003 0.0030 Durbin-watson 0 (For Number of Obs.) 1st Order Autocorrelation 0. 56 0.611 Non-White Male: Analysis of Variance Square F Value 182.13234 24.94194 20.0429 26.01891 0.51962 50.03 Dep 0.2085 8.12143 8.8589 0.896 0.8620 Parameter Standard T for HO: Variable Estimate Parameter=O Prob > JT: INTERCEP 1 5.2301 GNP 1 0.00993 GNP1 1 0.000569 GNP2 1-0.011396 UNEMP 1 0.108384 INF 1 0.028834 DOW 1 0.002463 WAR 1-0.363465 0.386889 0.0026253 0.00416014 0.0031149 0.02380352 0.03163 0.0005336 0.222502 13.813 3.664 0.13-3.658 4.3 0.910 4.615-1. 464 0.0006 0.8918 0.0006 0.362 0.1496 Durbin-watson D (For Number of Obs.) 1st Order Autocorrelation 0.988 56 0.456 1105
Non-White Female: OF Analysis of Variance Square F Value 16.4165.63165 21. 039.34525 0.09649 24.305 Oep C. V. 0.31063 2.28036 13.62211 Parameter Standard T for HO: variable OFEstimate Parameter=O INTERCEP 1 0.669291 0.16318641 4.101 GNP 1 0.003636 0.00115166 3.15 GNP1 1 0.000313 0.001921 0.15 GNP2 1-0.0083 0.00134232-3.63 UNEMP 1 0.0814 0.01025 8.268 INF 1 0.043084 0.01365060 3.156 DOW 1 0.00165 0.00023001.281 WAR 1 0.192540 0.10696658 1.800 Durbin-Watson D 1.295 (For Number of Obs.) 56 1st Order Autocorrelation 0.24 0.800 0.49 Prob > 0.0002 0.0028 0.8622 0.000 0.0028 0.081 ITI THE SAS RESULTS OF THE INVESTIGATION BASED UPON RACE. SEX. AND AGE The following tables contain summaries of findings. The results of 32 runnings (4 sets of sex and race, and 8 sets of ages) are condensed into four tables. The figures appearing in each cell correspond to statistical values of F, standard deviation, and correlation coefficient. The figures indicate the existence of a strong relationship between the suicide rate and economic factors. Variables/white Male (1930-1984) 5-14 15-24 25 34 35-44 45-54 -64 65 4 5 84 F-value 9.1 3.8 3.495 22.262.99 3.291 52.3 3.366 S.D. 0.203 21.2 465.36 1.931 2.631 196.42 4.11 215.3 R-Square 0.18 0.2 0. 0.8536 0.936 0.463 0.932.4685 Variables/Iolhite Female (1930 1984) 5-14 15 24 25-34 35-44 45-54 -64 65-4 5-84 F-value 8.811 23.816 16.92 12.016 9.365 14.431 12.1 4.91 S.D. 0.046 0.499 0.43 1.0445 1.054 0.6 0.81 0.92 R-Square 0.02 0.865 0.819 0.633 0.15 0.95 0.653 0.569 Variables/Non-Iolhite Male (1930-1984) 5-14 15 24 25 34 35 44 45-54 -64 65-4 5-84 F-value 3.2 30_53 36.34 1.491 6.330 3.952 3.21 1.454 S.D. 0.132 1.4 1.94 1.210 1.380 2.06 2.328 4.096 I R-Square 0.503 0.891 0.90 0.424 0.629 0.515 0.46 0.281 anaoles -,,~, 5 14 15 24 25-34 35-44 45-54 -64 65-4 5-84 F value.546 8.286 24.210 15.08.00 6.515 2.531 2.516 S.D. o.on 0.693 0.604 0.5 0.605 0.642 0.80 1.540 R'Square 0.669 0.689 0.86 0.802 0.61 0.63 0.404 0.403 1106
F-Value Suicide Rates ANOVA Values 10.---------------------------~------------------------, 10... --... -... -... -.. -.. -.. -.-------.-------~._.. -... --."... -.--.. -... -----------. ~ 0... -... -... --------.-.----.-.-... -... --.. -... -... --.-. 10... -....... ----------. --.......-.--... "-... -.... 10~... ~.. c._~~~-~----.~.-...--- to -.----...---.-.-.-.._-... o 6-14 16-24 26-34 315-44 415-64 Age Groups 66-64 66-4 6-84 White Male --- Non-White Male --+- White Female -- Non-White Female 0.8 0.6 0.4 Suicide Rates R-Square R-Sqaure 1.---~------------------------------------------------. 0_2.. --... ---.--... ---------------.-... ------.-.. ------- O+-------.------,r------.-------.-------.-------r----~ 6-14 16-24 26-34 315-44 415-154 Age Groups 615-64 615-4 15-84 White Male -- Non-White Male --+- White Female -- Non-White Female 110
SAS Analysis of the Findings: The findings of this study are interpreted in terms of the t-values, F-values, standards of deviation, and coefficients of correlation. For a.05 level of significance the population t-value is + 1.96 standard deviation. Looking at the results of the race and sex groups under the heading of"t for Ho: parameters = 0," we note that all suicide age categories are sensitive to unemployment. t values are positive, ranging from 4.5 to 13. This means unemployment contributes significantly to suicide rates. The negative t values for GNP. (2 years lag) show significant inverse relations for non-white male and nonwhite female. In other words, for non-white sex groups suicide rates fall as the level of GNP rises. The value of F measures the strength of the relationships between the y response (suicide rates) and the entire independent variables as a whole (economic factors and war). For a total of fifty-five observations and.05 level of significance, the population F-value equals 2.2. In order for the relationship to be significant the computed F-values for this study must exceed 2.2. A glance at the analysis of variance presented here indicates that the F-values range from 3.5 to 56, all of which are indicative of mild to a strong relationship between suicide rate and economic factors in general. With the exception of ages 25 to 34 and to 64 in the white male category, all figures of standard deviations are relatively small. The smallness of the standard deviation values in relation to the means of response figures (suicide rates of sexrace groups and age categories) is another indication of significant relationship. The coefficient of determination represented by shows the percentage variations explained by the model. The closer the value of to 1 or -1, the closer to perfect is the relationship between dependent and independent variables. The majority of R squares in this study falls into 60 or higher percentage. Surprisingly, race and sex groups of age categories 5-14 and 5-84 have shown little response to the economic factors used in the model. We may be inclined to state that most suicides fall into two age categories, and committed suicide for non-economic reasons. The study has also presented analysis of correlation under the headings of, Pearson Correlation. The intention is to determine whether there exists any multi colinearity among the independent variables. Should such colinearity be found among the variables, it would mean the extent and strength of the relationship between the Y response, i.e. the suicides due to the economic factors and the war have been exaggerated. The results presented here exhibit non- or mild colinearity. Each race and sex group is checked against the possible colinearity of GNP, unemployment, inflation, war and Dow Jones. In comparison to R = 1 the correlation coefficient seems too weak to suggest inter-linear relationship to exaggerate the influence of economic factors on the suicide rates. Summary and Conclusions: In the beginning of this paper, the hypothesis was in the form of this question: Do such aggregate factors such as GNP, unemployment, rate of inflation, and Dow Jones, have any direct or indirect bearing on the rate of suicides? According to the findings, these factors do play significant role in bringing the suicidal candidates to the edge. The extent of their contribution to suicide vary according to the sex, race, and age. The Pearson Correlation coefficients were low percentages indicating only slight correlation among economic factors themselves. This means that the Y response in the model was not exaggerated by the possible correlation between the economic factors in the model. One admits that if the data on suicide was purely due to economic variables, the results might have been more conclusive than the findings presented here. References: SAS Institute Inc., SAS/ETS User's Guide. 1982 Edition, Cary, NC: SAS Institute Inc., 1982. SAS Institute Inc., SAS System for Forecasting Time Series., 1986 Edition. 1108