Path: janda.org/c10 > Syllabus > Topics and Readings > Modeling Continuous Variables >
Multiple Regression & Log Transformations
Research Applications

Mueller: Multiple Regression & Logarithmic Transformation

John E. Mueller,
"Trends in Popular Support for the Wars in Korea and Vietnam,"
The American Political Science Review, 65 (June, 1971), 358-375.

Janda's note: Mueller studied the relationship between public support for these two wars over time. In both cases, public support declined over time. But why? Mueller hypothesized that support would decline as battlefield casualities increased. He showed that it did, but the relationship was more complex than most people would think.

Only a small portion of Mueller's article is reported here. Essentially, Mueller assembled all the poll data that he could find taken during the wars that asked people about their feelints toward the war. He had to use polls from different sources, often asking different questions. Table 1 displays a sample of questions that he used:

Table 1. Support and Opposition In the Korean War
A: "Do you think the United States made a mistake in going into the war in Korea, or not ?" (AIPO)
B: "Do you think the United States was right or wrong in sending American troops to stop the Communist invasion of South Korea?" (NORC)
D: "Looking back over the Korean War since it started last June (in June last year, last year, two years ago, in June of 1950) would you say now that you feel the United States (we) did the right thing in sending American forces to Korea?" (Minn.)

For each question [above] the numbers [below] represent, in order,
the percentages in support of the war (Pro), in opposition (Con), and with no opinion (DK).

Question A
Question B
Question D

Pro
Con
DK
Pro
Con
DK
Pro
Con
DK

July 1950

75
21
4

August 1950, Inchon landing

66b
19
15

September 1950, China enters

81
13
6

December 1950

39b
49
12
55
36
9
47d
42
11

February 1951

41
49
10
57
32
11

March1951, MacArthur recalled

43
44
13
60
30
10
46d
38
16


The follow text is extracted from Mueller, pp. 366-367:
[The Korean and Vietnam] wars . . . differed in the pace at which American casualties were suffered, As noted, Korea became an intense war in a few months while casualties in Vietnam mounted much more slowly. Support for the wars thus appears to be related to these casualty patterns, except that in the later stages of the wars the decline of support slowed despite continuously mounting casualties,

These observations can be formalized by viewing popular support as a function of the logarithm of the total number of American casualties that had been suffered at the time of the poll. As can be seen in Table 4, the regression equations so generated are strikingly similar for the two wars: In each war, support is projected to have started at much the same level and then every time American casualties increased by a factor of 10 (i.e., from 100 to 1,000 or from 10,000 to 100,000) support for the war dropped by about 15 percentage points. Results are not so neat when the dependent variable is the percentage opposing the war, but the patterns remain largely similar: Opposition to Vietnam is taken to have begun at a somewhat lower level than in Korea and then to have increased at a somewhat faster rate. Part of this difference is due to the generally lower frequencies of "no opinion" responses during the Vietnamese period.22


22. The similarities between the equations for the wars increase when one removes the NORC cases and the NORC dummy variable from the Korean consideration, thus comparing only questions almost identical for the two wars. The Korean equations then generate inter-cepts of 117.44 and -22.74 and regression coefficients of -15.51 and 13.40 for the approval and disapproval scores, respectively.

Table 4. Regression Results:
War Support as a Function of the Logarithm of American Casualties

Dependent variable

Percent support
Percent opposed

Korea
Vietnam
Korea
Vietnam
Mean
51.4
44.2
36.2
43.4
Standard Deviation
12.1
9.5
9.4
11.6

Intercept
114.46
121.68
-16.12
-52.05
Independent variables

Log10 Casualties
-14.89
-15.76
12.02
19.43

-2.38
-1.15
-2.6
-1.39
NORC dummy
15.49

-9.45

-2.1

-2.3
Standard error of estimate
5.21
3
5.68
365
R2
0.83
0.90
0.67
0.91

  • The regression equations are displayed vertically.
  • The number of items in the Korean case is 25: all items in Columns A and B of Table I except for that of September 1953 (which was taken after the war had ended).
  • The number of items in the Vietnam case iis 22: all items in Columns A and B of Table 3 after mid-1965 (which is when the war is taken to have begun for the American public).
  • The NORC dummy variable in the Korean case takes on a value of 1 if the item in question comes from Column B of Table 1 and is zero otherwise. It reflects therefore the general added boost given to measured war support by the wording of that question.
  • The figures in parentheses are the standard errors for the respective regression coefficients. To be regarded statistically significant a regression coefficient should be, conventionally, at least twice its standard error. All equations are significant (F test) at well beyond the .01 level.

When one takes support or opposition for the wars in Korea or Vietnam and correlates either of them with 1) the casualties suffered at the time the poll was conducted or 2) the duration of the war at the time of the poll (the plots in Figures 1 and 2), one gets at least a reasonably good fit; indeed, this would be the case if one correlated support or opposition with any variable that increased (or decreased) continually during the wars, But in all cases, correlating the logarithm of the number of casualties suffered at the time of the poll gives the best fit--the difference is especially noticeable in the Korean case. Furthermore, and most important, because of the differing patterns under which casualties were suffered in the two wars, the equations relating support or opposition to the logarithm of the casualties are much more similar for the two wars than are the equations generated when the logarithm of the casualties is replaced as the independent variable by the simple casualty figures or by the duration figures. The plots in Figures 1 and 2, relating support to duration, do not look greatly similar; if the percentage support were plotted against the logarithm of casualties, however, the lines would be highly similar for the two wars.

What this suggests, then, is that Americans, in the aggregate, reacted in similar ways to the two wars. While they did weary of the wars, they generally seem to have become hardened to the wars' costs; They are sensitive to rela-tively small losses in the early stages, but only to large losses in later stages. Another way of looking at the trends is to see subgroups of the population dropping off sequentially from the war's support as casualties mount. In the early stages the support of those with considerable misgivings is easily alienated; in later stages the only advocates left are the relatively hardened supporters whose conversion to opposition proves to be more difficult.