Sidney Cobb, David McFarland, Stanislav V. Kasl, George W. Brooks with the assistance of Patricia Tomlin

Transcription

1 The l-'ifih International Scientific Meeting of tho International Kpider.iiological Association, Au-UiiL' 25-31, 196S, Proceedings of the Interna tional npider.iolo^ical Association, Belgrade, Yugoslavie: Savremena Administracija, XH1-: :lk"lations III I 1 A.-iO^O VA1U AI'.LKS A LO..CTT!'DT.?:AL STUDY 01' PI-OPLl- CHANGING JOBS* LFBRAKY Sidney Cobb, David McFarland, Stanislav V. Kasl, George W. Brooks with the assistance of Patricia Tomlin Institute for SociaL Research University of Michigan Ann Arbor, Michigan, U.S.A. The research herein reported was supported in part by grants no 5-RO1-CD00102 and 1-K05-MH16,709 from the U.S. Public Health Service. This report is concerned with a methodologic problem in the analysis of data from a current longitudinal study of the health of people changing jobs. The objectives of this study are twofold: to describe the effects of the sudden termination of employment in middle life on physical health, mental health-and illness behavior, arn! to study the interrelationship of psychological and physiological variables as the men move through thia crisis in their lives. The data available for preliminary analysis involve 66 men who have been observed on five occasions from before the plant closing to one year after the closing. In this analysis we are concerned only with continuous variables collected in identical fashion, once at each time period. As might be expected, we have to deal with a certain amount of missing data because some of tho men were unavailable or refused at certain of the time periods. Forgetting about tho missing data, we can visualize the material as containing five observations on 66 men or 5 x data points. Because of missing data, we are in actuality dealing with about 250 :data points. In analyzing the relationship between any two variables we might simply calculate the correlation coefficient for those two variables over all those

2 -2- data points. However, the meaning of the correlation coefficient from such a calculation is not clear. It is of considerably more interest to know if the relationship between the two variables is due to the fact that they are associated characteristics of the individual or are properties of the individual that change together through time or both. We find it convenient to refer to the first as a static relationship and the second as a dynamic relationship. We recognize that a correlation using all the data points is some unidentifiable mixture of the two. We will, therefore, turn our attention to ways of estimating these static and dynamic relationships separately. There are two possible estimates of the static relationship and theoretically at least two for the dynamic relationship. These are displayed in table 1. First, one can take the means for the five observations on each individual for variable x and for variable y and correlate them. This gives us a correlation of ipsative means. This correlation has a static quality because the effect of time has been removed by averaging across time-.within individual. Second, one can calculate the deviations from these ipsative means and obtain ipsative deviations. When these ipsative deviations are correlated, one gets an estimate of the dynamic relationship because in the process of subtracting the man's mean from each of his several scores, one removes the characteristic of the man and leaves only the changes over time to be correlated. Third, one can calculate the mean at a single time across all men and obtain a normative mean. Theoretically, this should be an estimate of the dynamic relationship but practically this is only useful when one has a substantial number of observations on each man. In our study, we have only five observations per man and one is not usually comfortable about the estimation of a correlation from so small a number of points. Fourth, we can take these normative means and subtract them from each of the observations for the relevant time period and obtain a set of normative deviations. Correlations of normative deviations are.

3 -3- static in nature because the characteristic of the time period, that is the mean for that time period, has been subtracted out. Finally, it should be mentioned that forward differences, time one minus time two, are sometimes used as an estimate of the dynamic relationship. Such differences have a very large component of the random error of measurement. Obviously, a deviation score which is a mean minus a single observation has a relatively smaller error and a mean by itself has the least proportion of this random error. Turning to table 2 we see in the first line the relationships between the self report measure of anxiety and the self report measure of depression. To derive the figure of 0.72 in the column headed Ipsative Means, we take the mean of the five observations on each man so that we have a mean anxiety score and a mean depression score for each man and calculate the correlation between them. Next we take each man's mean anxiety score and subtract it from each of the five observations of anxiety on that man so that we have an ipsative deviation score for each data point, that is five for each man. Similarly, we obtain an ipsative deviation score for depression. When the two are correlated, we obtain the figure of 0.60 which appears in the last column. This indicates the degree to which changes over time in these variables are related. The normative deviations for the second column are obtained by calculating the mean anxiety for each time period and subtracting that from each of the 66 individual observations of anxiety for that time period. After doing the same for depression the two sets of scores are correlated yielding the value. of In the first row of the table, we have seen a pair of variables that have high static and high dynamic correlations. The next pair of variables, the self report of anxiety and the nurse's report of the man's anxiety shows an interesting and rather common pattern. The first estimate of the static

4 -4- relationship from the ipsative means, 0.60, is substantially higher than the correlation of the normative deviations, The difference between these two estimates of the static relationship is presumably due to the greater error of measurement in the deviations. Finally, there appears to be little, if any, dynamic relationship between these two variables. There are some possible reasons for this but they are technical and not relevant to this discussion. On the third line is a pair of variables that one would not expect to have much of a static relationship in the normal range^ for serum urate levels and serum creatinine levels are dependent on quite different metabolic pathways and yet. changes over time in kidney function could cause them to move together in a dynamic relationship. This notion is modestly supported by the negligible static correlations and the small but significant dynamic relationship. It should be added that this pattern is rare in our material. In summary, we have pointed to three patterns of association. First, the relation between anxiety and depression is both static and dynamic. Second, the relationship between the self report and the nurse report of anxiety is static but not dynamic. The third relationship between uric acid and creatinine in the serum is dynamic but not static. There are other ways that we might analyze such data. First, we might use the "indicator" or "dummy" variable approach to regression analysis (Suits, 1957). We dislike this because of the difficulty in interpretation of regression coefficients^ if one is without a specific causal hypothesis^ as to which of a pair of variables depends on the other. Second, we might look at the problem from the viewpoint of analysis of variance with repeated measures in which we would partition not only the variation in the several dependent variablesj but also the covariation between pairs of variables (Norman, 1967). This seems like a powerful approach but it is made difficult by the wide distribution

5 -5- of missing information in our data. Perhaps when more data are available, we may be able to establish a subset from which no information is missing. In the meantime, we are persisting in our efforts to find a way to solve the problem in the face of missing data and think that we are now on the verge of success. However, because of the simplicity with which correlation coefficients can be calculated on modern high speed computers^it is likely that we will persist in our interest in correlational estimates of the static and dynamic relations between variables in longitudinal studies. Before closing, we would like to remind ourselves that other variables may obscure or suppress a relationship, or an important relationship may be visible only in a particular subset of the population. Line four in the table illustrates a case in point. Here the expected relationship between anxiety and pulse rate is trivial until one restricts one's attention to those men who are at the flexible end of the California Personality Inventory scale of flexibility vs. rigidity. Parenthetically, it might be noted that this relation to pulse rate appears for the self report of anxiety, likewise only among the flexible. In conclusion, we hope that we have convinced the reader that the understanding of the relationship between variables in a longitudinal study is a complex matter and that trying to separate the static and the dynamic components of the relationship is worthwhile.

6 References Norman, W.T. On'estimating psychological relationships: social desirability and self report. Psychol. Bull. 67: , (1967). Suits, D.B. Use of dummy variables in regression equations. J. Am. Stat. Ass. 52: , (1957).

7 Table 1. The parameters from the data matrix of a longitudinal study that can be correlated to estimate static and dynamic relationships Static Relationship Dynamic Relationship Within each man across time Ipsative Means Ipsative Deviations At a single time across men Normative Deviations Normative Means Table 2. Comparison of the correlation coefficients for the ipsative means, the normative deviations and the ipsative deviations for the specified pairs of variables from a longitudinal study of people changing jobs. Static Dynamic Ipsative Normative Ipsative Means Deviations Deviations 1 Anxiety vs Depression Anxiety vs Nurse Report of Anxiety Serum Uric Acid vs Serum Creatinine Nurse Report of Anxiety vs Pulse Rate! Same for Rigid Men _ Same for Flexible Men 0.64

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