topic Re: Estimates for polynomial regression in proc glm in Statistical Procedures

Estimates for polynomial regression in proc glm

palolix — Wed, 13 Nov 2024 19:20:56 GMT

Dear SAS Community,

I am using a polynomial regression since the relationship between the outcome var DTR (continuous) and Harvest month (categorical) appears to be curvilinear. I would like to predict DTR (days to ripe) when the fruits were harvested in Jan (1) and Feb (2). Since I am not sure if my estimates are correct, I would greatly appreciate your feedback. I have seven harvest months in total (1,2,3,4,5,6,8).

ods graphics on;
proc glm data=one;
Where Wks<6;
class Harvest;
model DTR= Harvest Harvest*Harvest/solution alpha=.05 clparm;
estimate "pred DTR when Harvest=1" intercept 1 Harvest 1 0 0 0 0 0 0;
estimate "pred DTR when Harvest=2" intercept 1 Harvest 0 1 0 0 0 0 0;

run;
ods graphics off;

The GLM Procedure

Dependent Variable: DTR

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	6	2061.513304	343.585551	47.34	<.0001
Error	554	4020.971545	7.258071
Corrected Total	560	6082.484848

R-Square	Coeff Var	Root MSE	DTR Mean
0.338926	35.00184	2.694081	7.696970

Source	DF	Type I SS	Mean Square	F Value	Pr > F
Harvest	6	2061.513304	343.585551	47.34	<.0001

Source	DF	Type III SS	Mean Square	F Value	Pr > F
Harvest	6	2061.513304	343.585551	47.34	<.0001

Parameter	Estimate	Standard Error	t Value	Pr > \|t\|	95% Confidence Limits
pred DTR when Harvest=1	10.8666667	0.24593480	44.19	<.0001	10.3835879	11.3497454
pred DTR when Harvest=2	8.8292683	0.42074473	20.98	<.0001	8.0028182	9.6557184

Parameter	Estimate		Standard Error	t Value	Pr > \|t\|	95% Confidence Limits
Intercept	7.625000000	B	0.24593480	31.00	<.0001	7.141921263	8.108078737
Harvest 1	3.241666667	B	0.34780434	9.32	<.0001	2.558490165	3.924843169
Harvest 2	1.204268293	B	0.48735004	2.47	0.0138	0.246988411	2.161548175
Harvest 3	-0.075000000	B	0.49186961	-0.15	0.8789	-1.041157474	0.891157474
Harvest 4	-1.200000000	B	0.38885707	-3.09	0.0021	-1.963814549	-0.436185451
Harvest 5	-0.725000000	B	0.49186961	-1.47	0.1411	-1.691157474	0.241157474
Harvest 6	-2.250000000	B	0.34780434	-6.47	<.0001	-2.933176502	-1.566823498
Harvest 8	0.000000000	B	.	.	.	.	.

Note:

The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable.

Thank you very much!

Re: Estimates for polynomial regression in proc glm

Ksharp — Thu, 14 Nov 2024 02:40:45 GMT

"polynomial" is usually for continuous variable,not class variable, like :Quadratic/Cubic term .
why you have interact term 'Harvest*Harvest' in your model?

Re: Estimates for polynomial regression in proc glm

palolix — Thu, 14 Nov 2024 05:58:08 GMT

Thank you for replying! So outcome var and predictor var need to be continuous in order to fit a polynomial regression?

Re: Estimates for polynomial regression in proc glm

Ksharp — Thu, 14 Nov 2024 06:28:30 GMT

predictor var need to be continuous.
That is my opinion. I don't know if others would tell you another story.

Re: Estimates for polynomial regression in proc glm

palolix — Thu, 14 Nov 2024 06:45:04 GMT

Ok good to know. So since the relationship between my categorical predictor and outcome var is not linear and the distribution of residuals is skewed to the right I guess I will then fit a model with genmod using gamma or log transform the outcome var.
Thank you very much Ksharp!

Re: Estimates for polynomial regression in proc glm

Ksharp — Thu, 14 Nov 2024 07:03:03 GMT

categorical/nomial predictor and continuous outcome var can not have linear relationship.
linear relationship is just for two continuous variables.

Re: Estimates for polynomial regression in proc glm

palolix — Thu, 14 Nov 2024 19:00:11 GMT

Ok thank you, good to know.

So is this model appropriate for the categorical predictor Harvest (7 levels) and the continuous var DTR?

proc glm data=one order=freq ;
Where Wks<6;
class Harvest;
model DTR=Harvest /solution ss3 alpha=.05 clparm;
estimate "pred DTR when Harvest=1" intercept 1 Harvest 1 0 0 0 0 0 0;
estimate "pred DTR when Harvest=2" intercept 1 Harvest 0 1 0 0 0 0 0;
run;
quit;

The GLM Procedure

Dependent Variable: DTR

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	6	2061.513304	343.585551	47.34	<.0001
Error	554	4020.971545	7.258071
Corrected Total	560	6082.484848

R-Square	Coeff Var	Root MSE	DTR Mean
0.338926	35.00184	2.694081	7.696970

Source	DF	Type III SS	Mean Square	F Value	Pr > F
Harvest	6	2061.513304	343.585551	47.34	<.0001

Parameter	Estimate	Standard Error	t Value	Pr > \|t\|	95% Confidence Limits
pred DTR when Harvest=1	10.8666667	0.24593480	44.19	<.0001	10.3835879	11.3497454
pred DTR when Harvest=2	5.3750000	0.24593480	21.86	<.0001	4.8919213	5.8580787

Parameter	Estimate		Standard Error	t Value	Pr > \|t\|	95% Confidence Limits
Intercept	6.900000000	B	0.42597158	16.20	<.0001	6.063283083	7.736716917
Harvest 1	3.966666667	B	0.49186961	8.06	<.0001	3.000509192	4.932824141
Harvest 6	-1.525000000	B	0.49186961	-3.10	0.0020	-2.491157474	-0.558842526
Harvest 8	0.725000000	B	0.49186961	1.47	0.1411	-0.241157474	1.691157474
Harvest 4	-0.475000000	B	0.52170650	-0.91	0.3630	-1.499764753	0.549764753
Harvest 2	1.929268293	B	0.59873025	3.22	0.0013	0.753209236	3.105327350
Harvest 3	0.650000000	B	0.60241478	1.08	0.2811	-0.533296412	1.833296412
Harvest 5	0.000000000	B	.	.	.	.	.

Re: Estimates for polynomial regression in proc glm

Ksharp — Fri, 15 Nov 2024 00:56:58 GMT

Yeah. It looks good to me.
And you can simple your code by using LSMEANS instead of use ESTIMATE :

estimate "pred DTR when Harvest=1" intercept 1 Harvest 1 0 0 0 0 0 0;
estimate "pred DTR when Harvest=2" intercept 1 Harvest 0 1 0 0 0 0 0;
---->
lsmeans Harvest/cl ;

Re: Estimates for polynomial regression in proc glm

palolix — Fri, 15 Nov 2024 01:30:51 GMT

Great, thank you so much Ksharp!!