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SPSS FAQ
How can I compare regression coefficients between two groups?

Sometimes your research may predict that the size of a regression coefficient should be bigger for one group than for another. For example, you might believe that the regression coefficient of height predicting weight would be higher for men than for women. Below, we have a data file with 10 fictional females and 10 fictional males, along with their height in inches and their weight in pounds.

data list free
 / id * gender (A8) height * weight.
begin data.
 1   F  56 117
 2   F  60 125
 3   F  64 133
 4   F  68 141
 5   F  72 149
 6   F  54 109
 7   F  62 128
 8   F  65 131
 9   F  65 131
10   F  70 145
11   M  64 211
12   M  68 223
13   M  72 235
14   M  76 247
15   M  80 259
16   M  62 201
17   M  69 228
18   M  74 245
19   M  75 241
20   M  82 269
end data.
execute.

We analyzed their data separately using the regression commands below.  Note that we have to do two regressions, one with the data for females only and one with the data for males only.  We use a filter to separate the data into these two groups.  The parameter estimates (coefficients) for females and males are shown below, and the results do seem to suggest that height is a stronger predictor of weight for males (3.18) than for females (2.09).

COMPUTE filter_$=(gender="M").
FILTER BY filter_$.

regression
 /dep weight
 /method = enter height.

Variables Entered/Removed(b)

Model	Variables Entered	Variables Removed	Method
1	HEIGHT(a)	.	Enter
a All requested variables entered.
b Dependent Variable: WEIGH

 

Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.994(a)	.988	.987	2.40738
a Predictors: (Constant), HEIGHT

ANOVA(b)

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	3882.536	1	3882.536	669.926	.000(a)
	Residual	46.364	8	5.795
	Total	3928.900	9
a Predictors: (Constant), HEIGHT
b Dependent Variable: WEIGHT

Coefficients(a)

		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
Model		B	Std. Error	Beta
1	(Constant)	5.602	8.930		.627	.548
	HEIGHT	3.190	.123	.994	25.883	.000
a Dependent Variable: WEIGHT

COMPUTE filter_$=(gender="F").
FILTER BY filter_$.

regression
 /dep weight
 /method = enter height.

Variables Entered/Removed(b)

Model	Variables Entered	Variables Removed	Method
1	HEIGHT(a)	.	Enter
a All requested variables entered.
b Dependent Variable: WEIGHT

Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.989(a)	.978	.976	1.91504
a Predictors: (Constant), HEIGHT

ANOVA(b)

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	1319.561	1	1319.561	359.812	.000(a)
	Residual	29.339	8	3.667
	Total	1348.900	9
a Predictors: (Constant), HEIGHT
b Dependent Variable: WEIGHT

Coefficients(a)

		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
Model		B	Std. Error	Beta
1	(Constant)	-2.397	7.053		-.340	.743
	HEIGHT	2.096	.110	.989	18.969	.000
a Dependent Variable: WEIGHT

We can compare the regression coefficients of males with females to test the null hypothesis Ho: B_f = B_m, where B_f is the regression coefficient for females, and B_m is the regression coefficient for males.  To do this analysis, we first make a dummy variable called female that is coded 1 for female and 0 for male, and a variable femht that is the product of female and height. We then use female height and femht as predictors in the regression equation.

filter off.
execute.

compute female = 0.
if gender = "F" female = 1.
compute femht = female*height.
execute.

regression
 /dep weight
 /method = enter female height femht.

The output is shown below.

Variables Entered/Removed(b)

Model	Variables Entered	Variables Removed	Method
1	FEMHT, HEIGHT, FEMALE(a)	.	Enter
a All requested variables entered.
b Dependent Variable: WEIGHT

Model Summary

Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.999(a)	.999	.999	2.17518
a Predictors: (Constant), FEMHT, HEIGHT, FEMALE

ANOVA(b)

Model		Sum of Squares	df	Mean Square	F	Sig.
1	Regression	60327.097	3	20109.032	4250.111	.000(a)
	Residual	75.703	16	4.731
	Total	60402.800	19
a Predictors: (Constant), FEMHT, HEIGHT, FEMALE
b Dependent Variable: WEIGHT

Coefficients(a)

		Unstandardized Coefficients		Standardized Coefficients	t	Sig.
Model		B	Std. Error	Beta
1	(Constant)	5.602	8.069		.694	.497
	FEMALE	-7.999	11.371	-.073	-.703	.492
	HEIGHT	3.190	.111	.421	28.646	.000
	FEMHT	-1.094	.168	-.638	-6.520	.000
a Dependent Variable: WEIGHT

The term femht tests the null hypothesis Ho: B_f = B_m. The T value is -6.52 and is significant, indicating that the regression coefficient B_f is significantly different from B_m. 

Let's look at the parameter estimates to get a better understanding of what they mean and how they are interpreted. 
First, recall that our dummy variable female is 1 if female and 0 if male; therefore, males are the omitted group.  This is needed for proper interpretation of the estimates.

Parameter Variable Estimate INTERCEP 5.601677 : This is the intercept for the males (omitted group) This corresponds to the intercept for males in the separate groups analysis. FEMALE -7.999147 : Intercept Females - Intercept males This corresponds to differences of the intercepts from the separate groups analysis. and is indeed -2.397470040 - 5.601677149 HEIGHT 3.189727 : Slope for males (omitted group), i.e. Bm. FEMHT -1.093855 : Slope for females - Slope for males (i.e. Bf - Bm). From the separate groups, this is indeed 2.095872170 - 3.189727463 .

It is also possible to run such an analysis using glm, using syntax like that below.  Note that other statistical packages, such as SAS and Stata, omit the group of the dummy variable that is coded as zero. However, SPSS omits the group coded as one. Therefore, when you compare the output from the different packages, the results seem to be different. To make the SPSS results match those from other packages, you need to create a new variable that has the opposite coding (i.e., switching the zeros and ones). We do this with the male variable. We do not know of an option in SPSS glm to change which group is the omitted group.

compute male = not female.
compute maleht = male*height.
execute.

glm weight by male with height
 /design = male height male by height
 /print = parameter.

Between-Subjects Factors

		N
MALE	.00	10
	1.00	10

Tests of Between-Subjects Effects
Dependent Variable: WEIGHT

Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	60327.097(a)	3	20109.032	4250.111	.000
Intercept	.376	1	.376	.079	.782
MALE	2.342	1	2.342	.495	.492
HEIGHT	4695.831	1	4695.831	992.480	.000
MALE * HEIGHT	201.115	1	201.115	42.506	.000
Error	75.703	16	4.731
Total	733114.000	20
Corrected Total	60402.800	19
a R Squared = .999 (Adjusted R Squared = .999)

Parameter Estimates
Dependent Variable: WEIGHT

	B	Std. Error	t	Sig.	95% Confidence Interval
Parameter					Lower Bound	Upper Bound
Intercept	5.602	8.069	.694	.497	-11.504	22.707
[MALE=.00]	-7.999	11.371	-.703	.492	-32.104	16.105
[MALE=1.00]	0(a)	.	.	.	.	.
HEIGHT	3.190	.111	28.646	.000	2.954	3.426
[MALE=.00] * HEIGHT	-1.094	.168	-6.520	.000	-1.450	-.738
[MALE=1.00] * HEIGHT	0(a)	.	.	.	.	.
a This parameter is set to zero because it is redundant.

As you see, the glm output corresponds to the output obtained by regression. The parameter estimates appear at the end of the glm output. They also correspond to the output from regression.

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