[R-sig-ME] Inference in a mixed poisson models (resent, since I mailed in html format).

[Nilsson Fredrik X]

Dear All,

I have a data set where 22 laboratory rats have been treated with two
treatments (A and/or B). Then their brains have been cut into sections
and some cells (of a certain type) have been counted within a section
and every 6th section has been counted within each animal.

This has been done in two different regions in the brain (which gives
rise to msmtA resp. msmtB).

Now I have the following questions:
1. Would you analyze the cell types in the two different regions
separately? 
   If not, what model should one use?
2. How do one test for overdispersion in the model M2.lmer<-
   lmer(msmtB~tmtA*tmtB + (1|Animal), data=snitt2u, family=poisson)? (Or
for 
   that matter in M1.lmer<- lmer(msmtA~...) which seems to be more 
   overdispersed, but not so important for me).
3. What's the difference with a model M2.gee<-gee(msmtB~tmtA*tmtB, 
   id=Animal, data=snitt2u, family=poisson, corstr="AR-M")? And 
  a. which corstr to choose ("fixed" causes my computer to hang it
self)?   
     What correlation structure to use (if one could) is also relevant
for 
     the lmer.
  b. Is it correct in MASS (p.300) that the inference in a GLMM for the 
     beta's is on the individual level and for a GEE on the population 
     level? Seems strange to me... (but that's me).
  c. The gee gives much more significant "robust" z-values, how come?
  d. Do you trust gees anymore?
4. The structures that were measured on are somewhat ellipsoidal (resp.
the 
  shell of this structure), this could influence the number of
potentially 
  measured cells, what to do with that error?

I hope this is not too many, nor too silly questions!

Best regards,
Fredrik Nilsson

Data with rownumbers (collected in dataframe snitt2u above).
"Animal","msmtA","msmtB","Section","tmtA","tmtB"
"1","ind1",139,2,1,1,1
"2","ind1",123,0,7,1,1
"4","ind1",90,3,19,1,1
"5","ind1",118,2,25,1,1
"6","ind1",95,2,31,1,1
"7","ind1",118,2,37,1,1
"8","ind1",118,4,43,1,1
"9","ind1",107,4,49,1,1
"10","ind2",166,5,1,1,1
"11","ind2",150,0,7,1,1
"12","ind2",146,5,13,1,1
"13","ind2",109,3,19,1,1
"14","ind2",95,1,25,1,1
"15","ind2",98,1,31,1,1
"16","ind2",131,5,37,1,1
"17","ind2",112,1,43,1,1
"18","ind2",95,2,49,1,1
"19","ind2",117,0,55,1,1
"21","ind2",148,3,67,1,1
"22","ind2",108,2,73,1,1
"23","ind2",114,4,79,1,1
"24","ind2",67,0,85,1,1
"25","ind3",111,2,1,1,1
"26","ind3",95,6,7,1,1
"27","ind3",72,1,13,1,1
"28","ind3",93,5,19,1,1
"30","ind3",137,2,31,1,1
"31","ind3",109,3,37,1,1
"32","ind3",109,3,43,1,1
"33","ind3",84,4,49,1,1
"34","ind3",96,3,55,1,1
"35","ind3",105,2,61,1,1
"36","ind3",145,4,67,1,1
"37","ind3",120,1,73,1,1
"38","ind3",115,5,79,1,1
"39","ind3",82,4,85,1,1
"40","ind4",119,0,1,1,1
"41","ind4",70,0,7,1,1
"42","ind4",116,0,13,1,1
"43","ind4",197,1,19,1,1
"45","ind4",135,1,31,1,1
"46","ind4",149,1,37,1,1
"47","ind4",142,0,43,1,1
"48","ind4",90,1,49,1,1
"49","ind4",98,0,55,1,1
"50","ind4",102,0,61,1,1
"51","ind5",86,5,1,1,1
"52","ind5",117,6,7,1,1
"53","ind5",117,6,13,1,1
"55","ind5",126,5,25,1,1
"56","ind5",92,7,31,1,1
"57","ind5",113,2,37,1,1
"58","ind5",111,5,43,1,1
"59","ind5",131,11,49,1,1
"60","ind5",74,14,55,1,1
"61","ind5",111,2,61,1,1
"62","ind5",99,4,67,1,1
"63","ind6",166,2,1,1,1
"64","ind6",176,3,7,1,1
"65","ind6",177,0,13,1,1
"66","ind6",156,0,19,1,1
"67","ind6",128,1,25,1,1
"68","ind6",142,0,31,1,1
"69","ind6",78,0,37,1,1
"70","ind6",90,0,43,1,1
"72","ind6",187,1,55,1,1
"73","ind6",153,2,61,1,1
"74","ind6",119,1,67,1,1
"75","ind6",114,2,73,1,1
"76","ind6",93,1,79,1,1
"77","ind6",133,2,85,1,1
"78","ind6",93,2,91,1,1
"79","ind6",111,0,97,1,1
"80","ind7",24,0,1,0,1
"81","ind7",32,0,7,0,1
"82","ind7",21,0,13,0,1
"83","ind7",29,0,19,0,1
"84","ind7",33,0,25,0,1
"85","ind7",19,0,31,0,1
"86","ind7",25,0,37,0,1
"87","ind7",26,0,43,0,1
"88","ind7",28,0,49,0,1
"89","ind7",23,0,55,0,1
"90","ind7",33,0,61,0,1
"91","ind7",55,0,67,0,1
"93","ind7",41,0,79,0,1
"94","ind7",39,0,85,0,1
"95","ind9",33,0,1,0,1
"96","ind9",44,0,7,0,1
"97","ind9",25,0,13,0,1
"98","ind9",44,0,19,0,1
"99","ind9",26,0,25,0,1
"100","ind9",42,0,31,0,1
"102","ind9",27,0,43,0,1
"103","ind9",42,0,49,0,1
"104","ind9",12,0,55,0,1
"105","ind9",25,1,61,0,1
"106","ind9",23,0,67,0,1
"107","ind9",32,0,73,0,1
"108","ind10",19,0,1,0,1
"109","ind10",11,0,7,0,1
"110","ind10",16,0,13,0,1
"111","ind10",32,0,19,0,1
"112","ind10",10,0,25,0,1
"113","ind10",9,0,31,0,1
"114","ind10",13,0,37,0,1
"115","ind10",21,0,43,0,1
"116","ind11",15,0,1,0,1
"117","ind11",11,0,7,0,1
"118","ind11",19,0,13,0,1
"119","ind11",20,0,19,0,1
"120","ind11",16,1,25,0,1
"121","ind11",10,0,31,0,1
"122","ind11",7,0,37,0,1
"123","ind11",13,0,43,0,1
"124","ind12",17,0,1,0,1
"125","ind12",15,0,7,0,1
"126","ind12",15,0,13,0,1
"127","ind12",3,0,19,0,1
"129","ind12",12,0,31,0,1
"130","ind12",17,0,37,0,1
"131","ind12",10,0,43,0,1
"132","ind12",21,0,49,0,1
"133","ind12",13,0,55,0,1
"134","ind12",15,0,61,0,1
"135","ind12",30,0,67,0,1
"136","ind12",23,0,73,0,1
"137","ind12",14,0,79,0,1
"138","ind12",19,0,85,0,1
"139","ind13",137,47,1,1,0
"140","ind13",102,37,7,1,0
"141","ind13",126,41,13,1,0
"142","ind13",146,52,19,1,0
"143","ind13",102,35,25,1,0
"144","ind13",90,31,31,1,0
"145","ind13",90,40,37,1,0
"146","ind13",105,36,43,1,0
"148","ind13",93,59,55,1,0
"149","ind13",106,54,61,1,0
"150","ind13",101,62,67,1,0
"151","ind13",110,65,73,1,0
"152","ind14",157,79,1,1,0
"153","ind14",195,59,7,1,0
"154","ind14",209,54,13,1,0
"155","ind14",143,70,19,1,0
"156","ind14",142,41,25,1,0
"157","ind14",129,48,31,1,0
"158","ind14",124,74,37,1,0
"159","ind14",162,77,43,1,0
"160","ind14",114,70,49,1,0
"161","ind14",127,63,55,1,0
"162","ind14",101,65,61,1,0
"163","ind14",129,54,67,1,0
"164","ind15",131,54,1,1,0
"165","ind15",123,29,7,1,0
"166","ind15",93,26,13,1,0
"167","ind15",127,25,19,1,0
"168","ind15",187,28,25,1,0
"169","ind15",126,30,31,1,0
"170","ind15",116,29,37,1,0
"171","ind15",113,30,43,1,0
"173","ind15",128,55,55,1,0
"174","ind15",125,40,61,1,0
"175","ind15",97,19,67,1,0
"176","ind15",108,26,73,1,0
"177","ind15",240,52,79,1,0
"178","ind15",119,42,85,1,0
"179","ind15",120,53,91,1,0
"180","ind15",108,44,97,1,0
"181","ind16",172,119,1,1,0
"182","ind16",119,84,7,1,0
"183","ind16",118,79,13,1,0
"184","ind16",145,81,19,1,0
"186","ind16",143,74,31,1,0
"187","ind16",169,69,37,1,0
"188","ind16",131,57,43,1,0
"189","ind16",115,52,49,1,0
"190","ind16",136,53,55,1,0
"191","ind16",127,70,61,1,0
"192","ind16",151,56,67,1,0
"193","ind16",127,57,73,1,0
"194","ind16",94,54,79,1,0
"195","ind17",158,44,1,1,0
"196","ind17",173,48,7,1,0
"197","ind17",137,36,13,1,0
"198","ind17",157,61,19,1,0
"199","ind17",95,41,25,1,0
"200","ind17",133,47,31,1,0
"201","ind17",135,48,37,1,0
"202","ind17",125,41,43,1,0
"204","ind17",94,47,55,1,0
"205","ind17",106,45,61,1,0
"206","ind17",87,24,67,1,0
"207","ind17",95,37,73,1,0
"208","ind19",23,3,1,0,0
"209","ind19",35,0,7,0,0
"210","ind19",25,2,13,0,0
"211","ind19",25,1,19,0,0
"212","ind19",20,2,25,0,0
"213","ind19",26,4,31,0,0
"214","ind19",15,2,37,0,0
"215","ind19",14,1,43,0,0
"216","ind19",20,0,49,0,0
"217","ind19",10,0,55,0,0
"218","ind20",48,4,1,0,0
"219","ind20",34,2,7,0,0
"220","ind20",46,2,13,0,0
"221","ind20",43,5,19,0,0
"222","ind20",18,2,25,0,0
"223","ind20",41,3,31,0,0
"224","ind20",57,2,37,0,0
"225","ind20",43,2,43,0,0
"226","ind21",35,1,1,0,0
"227","ind21",35,2,7,0,0
"228","ind21",41,2,13,0,0
"229","ind21",30,2,19,0,0
"230","ind21",33,4,25,0,0
"231","ind21",41,3,31,0,0
"232","ind21",35,6,37,0,0
"233","ind21",38,2,43,0,0
"234","ind21",38,3,49,0,0
"235","ind21",56,1,55,0,0
"237","ind21",47,2,67,0,0
"238","ind21",50,3,73,0,0
"239","ind21",33,4,79,0,0
"240","ind21",32,2,85,0,0
"241","ind22",39,13,1,0,0
"242","ind22",47,9,7,0,0
"243","ind22",43,4,13,0,0
"245","ind22",46,9,25,0,0
"246","ind22",44,12,31,0,0
"247","ind22",43,5,37,0,0
"248","ind22",41,12,43,0,0
"249","ind23",40,3,1,0,0
"250","ind23",30,6,7,0,0
"252","ind23",45,4,19,0,0
"253","ind23",33,0,25,0,0
"254","ind23",31,0,31,0,0
"255","ind23",35,2,37,0,0
"256","ind23",24,3,43,0,0
"257","ind23",31,4,49,0,0
"258","ind23",30,1,55,0,0
"259","ind23",34,3,61,0,0
"260","ind23",50,0,67,0,0
"261","ind23",39,4,73,0,0
"262","ind23",57,0,79,0,0
"263","ind24",36,3,1,0,0
"264","ind24",48,8,7,0,0
"265","ind24",33,4,13,0,0
"266","ind24",51,1,19,0,0