Interpreting unstandardised coefficients where the independent variable is categorical

[jonathan rothwell]

Hello everyone,

I'm unsure of how to interpret unstandardised coefficients where the independent variable is categorical. In this case x is a categorical variable with values 1-4 that correspond to program characteristics around how strict conditionalities are enforced under conditional cash transfer programs, and y is the primary attendance effect size of 27 programs in percentage points. I have read that unstandardised coefficients should be interpreted as the corresponding change in x when there is a one unit increase in y. But this would mean that for every percentage point increase in attendance rates, the categorical variable moves up 1.8 values, but this makes no sense as there are only four values and the mean percentage point increase for 27 programs is around 5. Can anyone help with this interpretation? Please let me know if you need any more information.




Meta-reg primary Independent variable = primary attendance effect size

VARIABLES	(1)	(2)	(3)	(4)
Compliance Severity	0.280	1.578**	1.661**	1.804***
	(0.709)	(0.670)	(0.574)	(0.510)

[Richard Williams]

I have read that unstandardised coefficients should be interpreted as the corresponding change in x when there is a one unit increase in y

You've got it backwards. It should be

I have read that unstandardised coefficients should be interpreted as the corresponding change in y when there is a one unit increase in x

Since X is categorical, your coefficients would show you the dfference between being in category 2 vs 1, 3 vs 1, and 4 vs 1.

Showing the commands and output for the model you are estimating might further help. Use code tags. See pt. 12 in the FAQ. I would especially want to see if you are handling the categorical variable correctly.

[jonathan rothwell]

Hi Richard,

Thank you for your response. So if the independent variable is effect size in percentage points, then in regression 4, a one unit increase in compliance severity results in a 1.8% increase in attendance effect size, and a one unit increase in baseline enrolment (which is in decimal places in the dataset e.g. 0.75 rather than 75 (%) while attendance effect sizes are e.g. 13.2% rather than 0.132) results in a coefficient of -33.039, which after accounting for decimal places would mean a decrease of 3.3039%(or 0.33039%?) for every percentage point increase in attendance effect size. Supply component is a dummy equalling one if a program has supply side investment elements e.g. opening schools or hiring teachers, so programs with a supply component have 7% high attendance effect sizes? Am i on the right track now with this reasoning? I'm not sure it's necessary to show the fulls commands as I was just wondering about this one aspect of interpretation, but please do ask for them again if you think I may have gone wrong somewhere.

Kind regards,

Jon



Primary meta-regression Independent variable = primary attendance effect size

VARIABLES	(1)	(2)	(3)	(4)
Compliance Severity	0.280	1.578**	1.661**	1.804***
	(0.709)	(0.670)	(0.574)	(0.510)
LAC dummy		0.794	1.193
		(2.691)	(2.007)
Africa dummy		-0.790
		(3.675)
Meets evidence standards		-2.061	-2.219	-1.925
		(3.625)	(3.307)	(2.596)
Baseline enrolment		-34.305***	-33.674***	-33.039***
		(10.509)	(9.845)	(8.554)
Years of exposure		-0.148	-0.138	-0.104
		(0.468)	(0.442)	(0.296)
Mother dummy		-0.166	-0.152	0.490
		(2.472)	(2.318)	(1.757)
National dummy		-3.320	-3.385*	-3.539*
		(2.008)	(1.903)	(1.734)
Start-up dummy		-0.240	-0.058
		(2.067)	(1.825)
Payment frequency		0.797	0.356	1.339
		(3.231)	(2.482)	(1.790)
Average transfer		0.017	0.018	0.023
		(0.022)	(0.021)	(0.016)
Achievement conditionality		0.093	0.051	-0.066
		(2.266)	(2.116)	(1.880)
Supply component		6.020**	6.105**	7.015***
		(2.309)	(2.194)	(1.676)
Constant	2.755	32.019***	31.206***	29.395***
	(2.089)	(10.029)	(9.314)	(8.695)
Observations	27	27	27	27
Standard errors in parentheses			Table 9 Primary multiple meta-regression

[jonathan rothwell]

*The second sentence should read: 'So if the dependent variable is effect size in percentage points' rather than 'So if the independent variable is effect size in percentage points'