Table 17.1, page 447.
use https://stats.idre.ucla.edu/stat/stata/examples/cama4/depress, clear
gen incomecat = 0
replace incomecat = 1 if income >= 20
tab2 sex incomecat
| incomecat
sex | 0 1 | Total
-----------+----------------------+----------
male | 54 57 | 111
female | 125 58 | 183
-----------+----------------------+----------
Total | 179 115 | 294
Table 17.2, page 448.
table treat sex incomecat
--------------------------------------------
has a |
doctor |
prescribe |
d or |
recommend |
ed that |
you take |
medicine, | incomecat and sex
medical | ------ 0 ----- ------ 1 -----
treatment | male female male female
----------+---------------------------------
yes | 20 73 21 34
no | 34 52 36 24
--------------------------------------------
Table 17.3, page 449.
gen cesdcat = 0
replace cesdcat = 1 if cesd >=11
table treat sex incomecat, by(cesdcat)
--------------------------------------------
cesdcat |
and has a |
doctor |
prescribe |
d or |
recommend |
ed that |
you take |
medicine, | incomecat and sex
medical | ------ 0 ----- ------ 1 -----
treatment | male female male female
----------+---------------------------------
0 |
yes | 16 48 16 20
no | 23 33 30 20
----------+---------------------------------
1 |
yes | 4 25 5 14
no | 11 19 6 4
--------------------------------------------
Page 451 middle of the page.
NOTE: You will need to download the tabchi ado, which can be installed by typing search tabchi in the command line (see How can I use the search command to search for programs and get additional help? for more information about using search).
tabchi sex incomecat
observed frequency
expected frequency
----------------------------
| incomecat
sex | 0 1
----------+-----------------
male | 54 57
| 67.582 43.418
|
female | 125 58
| 111.418 71.582
----------------------------
Pearson chi2(1) = 11.2104 Pr = 0.001
likelihood-ratio chi2(1) = 11.1467 Pr = 0.001
Page 454. Ttop of the page.
tab2 sex incomecat, chi2
| incomecat
sex | 0 1 | Total
-----------+----------------------+----------
male | 54 57 | 111
female | 125 58 | 183
-----------+----------------------+----------
Total | 179 115 | 294
Pearson chi2(1) = 11.2104 Pr = 0.001
Table 17.7, page 455.
NOTE: The xi3 program needs to be downloaded and installed. You can use the search command to find the program and follow the directions given for downloading and installing it (see How can I use the search command to search for programs and get additional help? for more information about using search).
collapse (count) id, by(sex incomecat)
rename id count
recode sex 1=0 2=1
xi3: glm count d.sex*d.incomecat, fam(pois)
d.sex _Isex_0-1 (naturally coded; _Isex_0 omitted)
d.incomecat _Iincomecat_0-1 (naturally coded; _Iincomecat_0 omitted)
d.sex*d.incom~t _IsexXinc_#_# (coded as above)
Iteration 0: log likelihood = -12.201957
Iteration 1: log likelihood = -12.14127
Iteration 2: log likelihood = -12.141259
Iteration 3: log likelihood = -12.141259
Generalized linear models No. of obs = 4
Optimization : ML: Newton-Raphson Residual df = 0
Scale param = 1
Deviance = 4.44089e-16 (1/df) Deviance = .
Pearson = 1.72033e-27 (1/df) Pearson = .
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -12.14125876 AIC = 8.070629
BIC = 4.44089e-16
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Isex_1 | .2141804 .061899 3.46 0.001 .0928606 .3355001
_Iincomeca~1 | -.1784509 .061899 -2.88 0.004 -.2997707 -.0571311
_IsexXinc_~1 | -.2054845 .061899 -3.32 0.001 -.3268043 -.0841647
_cons | 4.230198 .061899 68.34 0.000 4.108878 4.351518
------------------------------------------------------------------------------
Page 461.
use "c:cama4depress.dta", clear gen incomecat = 0 replace incomecat = 1 if income >= 20 (115 real changes made) collapse (count) beddays, by(sex incomecat treat ) rename beddays count
NOTE: These are in the reverse order so that the subtraction is done correctly. The lrtest commands give the likelihood ratio tests and the display commands give the Pearson tests. To determine the number of degrees of freedom shown in the display chi2tail commands, you need to subtract the number of degrees of freedom for the two models in the comparison.
xi3: glm count sex*incomecat*treat, fam(poi)
This is an experimental version of xi3
Please view results with some caution
Iteration 0: log likelihood = -21.561163
Iteration 1: log likelihood = -21.421271
Iteration 2: log likelihood = -21.421201
Iteration 3: log likelihood = -21.421201
Generalized linear models No. of obs = 8
Optimization : ML: Newton-Raphson Residual df = 0
Scale param = 1
Deviance = 1.44329e-14 (1/df) Deviance = .
Pearson = 8.09169e-24 (1/df) Pearson = .
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -21.42120107 AIC = 7.3553
BIC = 1.44329e-14
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sex | 2.164571 .5508512 3.93 0.000 1.084923 3.24422
incomecat | .8358518 1.422674 0.59 0.557 -1.952538 3.624242
treat | 1.400472 .592095 2.37 0.018 .2399874 2.560957
_IseXin | -.7954299 .8252301 -0.96 0.335 -2.412851 .8219915
_IseXtr | -.869844 .3351733 -2.60 0.009 -1.526772 -.2129163
_IinXtr | .0258275 .8504365 0.03 0.976 -1.640997 1.692652
_IseXinXtr | -.0174592 .50874 -0.03 0.973 -1.014571 .9796529
_cons | .3005329 .9958275 0.30 0.763 -1.651253 2.252319
------------------------------------------------------------------------------
lrtest, saving(m0)
xi3: glm count sex*incomecat sex*treat incomecat*treat, fam(poi)
This is an experimental version of xi3
Please view results with some caution
Iteration 0: log likelihood = -21.554923
Iteration 1: log likelihood = -21.42186
Iteration 2: log likelihood = -21.42179
Iteration 3: log likelihood = -21.42179
Generalized linear models No. of obs = 8
Optimization : ML: Newton-Raphson Residual df = 1
Scale param = 1
Deviance = .001177818 (1/df) Deviance = .0011778
Pearson = .0011777657 (1/df) Pearson = .0011778
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -21.42178998 AIC = 7.105447
BIC = -2.078263724
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sex | 2.176457 .4288301 5.08 0.000 1.335965 3.016948
incomecat | .8798374 .6176395 1.42 0.154 -.3307138 2.090389
_IseXin | -.8223852 .2533633 -3.25 0.001 -1.318968 -.3258023
treat | 1.413416 .4567266 3.09 0.002 .5182485 2.308584
_IseXtr | -.877427 .252167 -3.48 0.001 -1.371665 -.3831887
_IinXtr | -.0020759 .2493924 -0.01 0.993 -.490876 .4867242
_cons | .2799075 .7951472 0.35 0.725 -1.278552 1.838367
------------------------------------------------------------------------------
lrtest, using(m0)
Glm: likelihood-ratio test chi2(1) = 0.00
Prob > chi2 = 0.9726
di .0011777657 - 0
.00117777
di chi2tail(1, .00117777)
.97262305
lrtest, saving(m1)
glm count sex incomecat treat, fam(poi)
Iteration 0: log likelihood = -33.613736
Iteration 1: log likelihood = -33.459453
Iteration 2: log likelihood = -33.459367
Iteration 3: log likelihood = -33.459367
Generalized linear models No. of obs = 8
Optimization : ML: Newton-Raphson Residual df = 4
Scale param = 1
Deviance = 24.07633241 (1/df) Deviance = 6.019083
Pearson = 24.6518747 (1/df) Pearson = 6.162969
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -33.45936727 AIC = 9.364842
BIC = 15.75856624
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sex | .499956 .1203058 4.16 0.000 .2641609 .735751
incomecat | -.4424537 .1195083 -3.70 0.000 -.6766857 -.2082216
treat | -.0136057 .1166451 -0.12 0.907 -.2422258 .2150145
_cons | 3.040618 .2723247 11.17 0.000 2.506872 3.574365
------------------------------------------------------------------------------
di 24.6518747 - .0011777657
24.650697
di chi2tail(3, 24.650697)
.00001827
lrtest, using(m1)
Glm: likelihood-ratio test chi2(3) = 24.08
Prob > chi2 = 0.0000
lrtest, saving(m2)
glm count, fam(poi)
Iteration 0: log likelihood = -49.483935
Iteration 1: log likelihood = -49.394894
Iteration 2: log likelihood = -49.394881
Iteration 3: log likelihood = -49.394881
Generalized linear models No. of obs = 8
Optimization : ML: Newton-Raphson Residual df = 7
Scale param = 1
Deviance = 55.94736055 (1/df) Deviance = 7.99248
Pearson = 61.31972823 (1/df) Pearson = 8.759961
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -49.39488135 AIC = 12.59872
BIC = 41.39126976
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 3.604138 .0583212 61.80 0.000 3.489831 3.718446
------------------------------------------------------------------------------
lrtest, using(m2)
Glm: likelihood-ratio test chi2(3) = 31.87
Prob > chi2 = 0.0000
di 61.31972823 - 24.6518747
36.667854
di chi2tail(3, 36.667854)
5.409e-08
Page 462 table in the middle of the page.
NOTE: The first poisson and lrtest commands are used to calculate and save the model to which the other three models will be compared. We have used the quietly command to suppress the output of the poisson command, as it is not needed.
Partial association:
quietly xi3: poisson count sex*treat incomecat*treat sex*incomecat
lrtest, saving(m0)
quietly xi3: poisson count sex*treat incomecat*treat incomecat
lrtest, using(m0)
Poisson: likelihood-ratio test chi2(1) = 10.67
Prob > chi2 = 0.0011
quietly xi3: poisson count sex*treat incomecat*sex incomecat
lrtest, using(m0)
Poisson: likelihood-ratio test chi2(1) = 0.00
Prob > chi2 = 0.9934
quietly xi3: poisson count sex*incomecat incomecat*treat incomecat
lrtest, using(m0)
Poisson: likelihood-ratio test chi2(1) = 12.45
Prob > chi2 = 0.0004
Marginal association:
tabchi sex incomecat [weight=count]
(frequency weights assumed)
observed frequency
expected frequency
----------------------------
| incomecat
sex | 0 1
----------+-----------------
male | 54 57
| 67.582 43.418
|
female | 125 58
| 111.418 71.582
----------------------------
Pearson chi2(1) = 11.2104 Pr = 0.001
likelihood-ratio chi2(1) = 11.1467 Pr = 0.001
tabchi sex treat [weight=count]
(frequency weights assumed)
observed frequency
expected frequency
--------------------------
| has a doctor
| prescribed or
| recommended
| that you take
| medicine,
| medical
| treatment
sex | yes no
----------+---------------
male | 41 70
| 55.878 55.122
|
female | 107 76
| 92.122 90.878
--------------------------
Pearson chi2(1) = 12.8149 Pr = 0.000
likelihood-ratio chi2(1) = 12.9284 Pr = 0.000
tabchi incomecat treat [weight=count]
(frequency weights assumed)
observed frequency
expected frequency
--------------------------
| has a doctor
| prescribed or
| recommended
| that you take
| medicine,
| medical
| treatment
incomecat | yes no
----------+---------------
0 | 93 86
| 90.109 88.891
|
1 | 55 60
| 57.891 57.109
--------------------------
Pearson chi2(1) = 0.4776 Pr = 0.490
likelihood-ratio chi2(1) = 0.4777 Pr = 0.489
Page 464 table in the middle of the page.
NOTE: For the first four entries in the table, the poisson command can be used to generate the likelihood ratio chi-squared. For the rest of the table, the lrtest command provides the entries in the table. We have used the quietly command for the corresponding poisson command to suppress the output, as we are only interested in the output of the lrtest commands.
The first-order terms:
poisson count incomecat
Iteration 0: log likelihood = -86.914684
Iteration 1: log likelihood = -86.914684
Poisson regression Number of obs = 16
LR chi2(1) = 14.04
Prob > chi2 = 0.0002
Log likelihood = -86.914684 Pseudo R2 = 0.0748
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
incomecat | -.4424537 .1195083 -3.70 0.000 -.6766857 -.2082216
_cons | 3.107944 .0747435 41.58 0.000 2.96145 3.254439
------------------------------------------------------------------------------
poisson count sex
Iteration 0: log likelihood = -85.03012
Iteration 1: log likelihood = -85.03012
Poisson regression Number of obs = 16
LR chi2(1) = 17.81
Prob > chi2 = 0.0000
Log likelihood = -85.03012 Pseudo R2 = 0.0948
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sex | .499956 .1203058 4.16 0.000 .2641609 .735751
_cons | 2.130133 .2037168 10.46 0.000 1.730855 2.52941
------------------------------------------------------------------------------
poisson count treat
Iteration 0: log likelihood = -93.929955
Iteration 1: log likelihood = -93.929955
Poisson regression Number of obs = 16
LR chi2(1) = 0.01
Prob > chi2 = 0.9071
Log likelihood = -93.929955 Pseudo R2 = 0.0001
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
treat | -.0136057 .1166451 -0.12 0.907 -.2422258 .2150145
_cons | 2.931376 .1840553 15.93 0.000 2.570635 3.292118
------------------------------------------------------------------------------
poisson count cesdcat
Iteration 0: log likelihood = -69.575822
Iteration 1: log likelihood = -69.575808
Iteration 2: log likelihood = -69.575808
Poisson regression Number of obs = 16
LR chi2(1) = 48.72
Prob > chi2 = 0.0000
Log likelihood = -69.575808 Pseudo R2 = 0.2593
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cesdcat | -.8505394 .1273499 -6.68 0.000 -1.100141 -.6009381
_cons | 3.248435 .0696733 46.62 0.000 3.111877 3.384992
------------------------------------------------------------------------------
The second-order terms:
NOTE: The first lrtest is used to save the model to which all of the other models in this section will be compared.
quietly xi3: poisson count sex*treat sex*incomecat sex*cesdcat treat*incomecat ///
treat*cesdcat incomecat*cesdcat
lrtest, saving(m2)
quietly poisson count sex treat incomecat cesdcat _IseXtr _IseXce _ItrXin _ItrXce _IinXce
lrtest, using(m2)
Poisson: likelihood-ratio test chi2(1) = 9.91
Prob > chi2 = 0.0016
quietly poisson count sex treat incomecat cesdcat _IseXtr _IseXin _IseXce _ItrXce _IinXce
lrtest, using(m2)
Poisson: likelihood-ratio test chi2(1) = 0.00
Prob > chi2 = 0.9653
quietly poisson count sex treat incomecat cesdcat _IseXtr _IseXin _IseXce _ItrXin _ItrXce
lrtest, using(m2)
Poisson: likelihood-ratio test chi2(1) = 1.17
Prob > chi2 = 0.2799
quietly poisson count sex treat incomecat cesdcat _IseXin _IseXce _ItrXin _ItrXce _IinXce
lrtest, using(m2)
Poisson: likelihood-ratio test chi2(1) = 11.98
Prob > chi2 = 0.0005
quietly poisson count sex treat incomecat cesdcat _IseXtr _IseXin _ItrXin _ItrXce _IinXce
lrtest, using(m2)
Poisson: likelihood-ratio test chi2(1) = 2.34
Prob > chi2 = 0.1259
quietly poisson count sex treat incomecat cesdcat _IseXtr _IseXce _IseXin _ItrXin _IinXce
lrtest, using(m2)
Poisson: likelihood-ratio test chi2(1) = 0.32
Prob > chi2 = 0.5733
Third-order terms:
quietly xi3: poisson count sex*treat*incomecat sex*treat*cesdcat ///
sex*incomecat*cesdcat treat*incomecat*cesdcat
lrtest, saving(m3)
quietly poisson count sex treat incomecat cesdcat _IseXin _IseXtr _IseXce _ItrXin _ItrXce _IinXce ///
_IseXtrXce _IseXinXce _ItrXinXce
lrtest, using(m3)
Poisson: likelihood-ratio test chi2(1) = 0.01
Prob > chi2 = 0.9274
quietly poisson count sex treat incomecat cesdcat _IseXin _IseXtr _IseXce _ItrXin _ItrXce _IinXce ///
_IseXtrXin _IseXtrXce _ItrXinXce
lrtest, using(m3)
Poisson: likelihood-ratio test chi2(1) = 0.01
Prob > chi2 = 0.9205
quietly poisson count sex treat incomecat cesdcat _IseXin _IseXtr _IseXce _ItrXin _ItrXce _IinXce ///
_IseXtrXin _IseXtrXce _IseXinXce
lrtest, using(m3)
Poisson: likelihood-ratio test chi2(1) = 4.74
Prob > chi2 = 0.0294
quietly poisson count sex treat incomecat cesdcat _IseXin _IseXtr _IseXce _ItrXin _ItrXce _IinXce ///
_IseXtrXin _IseXinXce _ItrXinXce
lrtest, using(m3)
Poisson: likelihood-ratio test chi2(1) = 1.23
Prob > chi2 = 0.2680
Page 468.
use https://stats.idre.ucla.edu/stat/stata/examples/cama4/depress, clear
gen incomecat = 0
replace incomecat = 1 if income >= 20
collapse (count) id, by(sex incomecat treat)
rename id count
recode sex 2=0
recode treat 2=0
recode incomecat 0=1 1= 0
xi3: glm count d.sex*d.treat d.treat*d.incomecat d.sex*d.incomecat, fam(pois)
d.sex _Isex_0-1 (naturally coded; _Isex_0 omitted)
d.treat _Itreat_0-1 (naturally coded; _Itreat_0 omitted)
d.incomecat _Iincomecat_0-1 (naturally coded; _Iincomecat_0 omitted)
Iteration 0: log likelihood = -21.554923
Iteration 1: log likelihood = -21.42186
Iteration 2: log likelihood = -21.42179
Iteration 3: log likelihood = -21.42179
Generalized linear models No. of obs = 8
Optimization : ML: Newton-Raphson Residual df = 1
Scale param = 1
Deviance = .001177818 (1/df) Deviance = .0011778
Pearson = .0011777657 (1/df) Pearson = .0011778
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -21.42178998 AIC = 7.105447
BIC = -2.078263724
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Isex_1 | -.2245618 .0635601 -3.53 0.000 -.3491373 -.0999863
_Itreat_1 | -.0481189 .0627327 -0.77 0.443 -.1710728 .0748349
_Ise1Xtr1 | -.2193567 .0630417 -3.48 0.001 -.3429163 -.0957972
_Iincomeca~1 | .1784271 .0619647 2.88 0.004 .0569785 .2998757
_Itr1Xin1 | -.000519 .0623481 -0.01 0.993 -.122719 .1216811
_Ise1Xin1 | -.2055963 .0633408 -3.25 0.001 -.329742 -.0814506
_cons | 3.512079 .0635747 55.24 0.000 3.387475 3.636683
------------------------------------------------------------------------------
Page 470 top of the page.
use https://stats.idre.ucla.edu/stat/stata/examples/cama4/depress, clear
gen treat1 = treat - 1
gen sex1 = sex -1
logit treat1 sex1 incomecat
=Iteration 0: log likelihood = -203.77847
Iteration 1: log likelihood = -197.31646
Iteration 2: log likelihood = -197.31424
Logit estimates Number of obs = 294
LR chi2(2) = 12.93
Prob > chi2 = 0.0016
Log likelihood = -197.31424 Pseudo R2 = 0.0317
------------------------------------------------------------------------------
treat1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sex1 | -.877427 .2521666 -3.48 0.001 -1.371664 -.3831895
incomecat | -.0020759 .2493921 -0.01 0.993 -.4908755 .4867237
_cons | .5359893 .2347028 2.28 0.022 .0759804 .9959983
------------------------------------------------------------------------------