topic Poisson's Regression equation (e^B0+B1x1????)with Generalized Linear Model in Discussions
https://community.jmp.com/t5/Discussions/Poisson-s-Regression-equation-e-B0-B1x1-with-Generalized-Linear/m-p/307999#M56240
<P>Hi can someone give me a hand?</P><P>So we are doing Poisson's Regression right now- we were asked to use the Generalized Linear Model - Distribution: Poisson's - Link function: log. My teacher has asked to write the regression equation with no guidance on how to do so. His advice was go do it in SAS, which would be useful if 1). I had a SAS license and 2). knew how to code in SAS. But without those I am left to JMP, which is in fact what the class is about so hopefully my frustration is understood.</P><P> </P><P>I understand its theoretically "linear" and I understand log is used for our link but can someone help me write it out. I am finding conflicting errors online and I can't complete any of my homework with out this. </P><P> </P><P>My y variable is Length of Stay in hospital, my X-variable is number of factors (number of medical items used during stay) My parameters are as followed:</P><P> </P><P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="poisson.PNG" style="width: 734px;"><img src="https://community.jmp.com/t5/image/serverpage/image-id/26783iEE51D8DDB6B63839/image-size/large?v=1.0&px=999" title="poisson.PNG" alt="poisson.PNG" /></span></P><P> </P><P>I attempted to use the "prediction formula column to give me the formula, which said e^B0+B1x1 --> e^1.392+0.0021x. Is this what it is? </P><P> </P><P>Also if whoever answers this has a solid understanding on Poisson's, I have an additional question on model adequacy.</P><P> </P><P>THANK YOU </P><P>#STATISTICS </P>Tue, 15 Sep 2020 21:55:38 GMTrlw2682020-09-15T21:55:38ZPoisson's Regression equation (e^B0+B1x1????)with Generalized Linear Model
https://community.jmp.com/t5/Discussions/Poisson-s-Regression-equation-e-B0-B1x1-with-Generalized-Linear/m-p/307999#M56240
<P>Hi can someone give me a hand?</P><P>So we are doing Poisson's Regression right now- we were asked to use the Generalized Linear Model - Distribution: Poisson's - Link function: log. My teacher has asked to write the regression equation with no guidance on how to do so. His advice was go do it in SAS, which would be useful if 1). I had a SAS license and 2). knew how to code in SAS. But without those I am left to JMP, which is in fact what the class is about so hopefully my frustration is understood.</P><P> </P><P>I understand its theoretically "linear" and I understand log is used for our link but can someone help me write it out. I am finding conflicting errors online and I can't complete any of my homework with out this. </P><P> </P><P>My y variable is Length of Stay in hospital, my X-variable is number of factors (number of medical items used during stay) My parameters are as followed:</P><P> </P><P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="poisson.PNG" style="width: 734px;"><img src="https://community.jmp.com/t5/image/serverpage/image-id/26783iEE51D8DDB6B63839/image-size/large?v=1.0&px=999" title="poisson.PNG" alt="poisson.PNG" /></span></P><P> </P><P>I attempted to use the "prediction formula column to give me the formula, which said e^B0+B1x1 --> e^1.392+0.0021x. Is this what it is? </P><P> </P><P>Also if whoever answers this has a solid understanding on Poisson's, I have an additional question on model adequacy.</P><P> </P><P>THANK YOU </P><P>#STATISTICS </P>Tue, 15 Sep 2020 21:55:38 GMThttps://community.jmp.com/t5/Discussions/Poisson-s-Regression-equation-e-B0-B1x1-with-Generalized-Linear/m-p/307999#M56240rlw2682020-09-15T21:55:38ZRe: Poisson's Regression equation (e^B0+B1x1????)with Generalized Linear Model
https://community.jmp.com/t5/Discussions/Poisson-s-Regression-equation-e-B0-B1x1-with-Generalized-Linear/m-p/311149#M56437
<P>Parameter Estimates and the Saved Prediction Formula</P>
<P><span class="lia-inline-image-display-wrapper lia-image-align-inline" image-alt="Screen Shot 2020-09-22 at 3.21.29 PM.png" style="width: 528px;"><img src="https://community.jmp.com/t5/image/serverpage/image-id/26920iD867DC968DB365EC/image-size/large?v=1.0&px=999" title="Screen Shot 2020-09-22 at 3.21.29 PM.png" alt="Screen Shot 2020-09-22 at 3.21.29 PM.png" /></span></P>
<P>This is in JMP v15. Maybe in earlier versions of JMP the formula was expressed differently.</P>
<P>Since the link function is Log, the prediction must be exponentiated back to units of X.</P>
<P> </P>
<P>Not a Poisson expert, but its a fun distribution because the center and scale parameters are equal. So when X is big it looks normal, and when X is close to 0 it looks log normal.</P>
<P> </P>
<P>This is from the scripting index, super useful for understanding the behavior of the distribution at different levels of lambda</P>
<PRE><CODE class=" language-jsl">Names Default To Here( 1 );
lambda = 4;
New Window( "Example: Poisson Probability",
pdy = Graph Box(
Y Scale( 0, 0.20 ),
X Scale( -1, 40 ),
Pen Color( "red" ),
Pen Size( 2 );
For( k = 0, k <= 40, k++,
V Line(
k,
0,
Poisson Probability( lambda, k )
)
);
Text(
{30, 0.18},
"\!U03BB=",
Round( lambda, 2 )
);
),
H List Box(
Slider Box( 0, 40, lambda, pdy << reshow ),
Text Box( " \!U03BB" )
)
);</CODE></PRE>Tue, 22 Sep 2020 19:27:05 GMThttps://community.jmp.com/t5/Discussions/Poisson-s-Regression-equation-e-B0-B1x1-with-Generalized-Linear/m-p/311149#M56437Byron_JMP2020-09-22T19:27:05Z