Sunday, May 22, 2016

Logistic Regression

The analysis is based on the Gapminder codebook containing 15 socio-economic factors from 2007 drawn from 213 countries. The analysis was generated using SAS StudioI chose to review the correlation between the female employ rate (a quantitative response variable) and the urban rate. This analysis also includes several additional quantitative explanatory variables in the Gapminder dataset, including the income per person, internet use rate, polity score, life expectancy end employ rate. The Logistic procedure is used to create regression models that describe the relationships between a binary response variable (female employ rate) and the set of predictor variables. 
  1. Country was added as an explanatory variable in the GLM procedure. Effective coding or parameterization was applied to the country attribute to create 6 explanatory categories and allow for group comparisons. The countries were categorized into 6 continental groups: Africa(0), Asia(1), Europe(2), North America(3), Oceania(4), South America(5).
  2. The quantitative explanatory variables were standardized for the GLM and Logistic procedures.
  3. The categorical response variable female employ was created from the quantitative variable as follows: Female employ rates < 50% = 0 and Female employ rates >= 50% = 1. This was used in the Logistic procedure.
Summary of Findings
  1. The GLM procedure shows the female employment rate is significantly correlated with the urban rate, income per person, polity score, life expectancy and employ rate. There is no correlation with internet use rate.
  2. When African countries are the reference explanatory group, only the European countries are statistically different.
  3. When Asian countries are the reference explanatory group, only the European countries are statistically different.
  4. When European countries are the reference explanatory group, all countries, except Oceanic countries, are statistically different.
  5. When North American countries are the reference explanatory group, only the European countries are statistically different.
  6. When Oceanic countries are the reference explanatory group, none of the other countries are statistically different.
  7. When South American countries are the reference explanatory group, only the European countries are statistically different.
  8. The Logistic procedure shows that countries with higher urban rates are have a 0.98 more likely to have female employ rates below 50% (parameter estimate = -.0164, p-value=0.0094, odds ratio=0.984). We can say with 95% confidence that the likelihood lies between 0.972 and 0.996.
  9. Adding income per person and controlling for urban rate shows no statistical significance. Adding internet use rate shows a similar result. However, this confounds the relationship between urban rate and the response category. Polity score and life expectancy also show statistical significance when controlling for the other explanatory variables.
  10. The employ rate explanatory variable (parameter estimate=0.3, p-value <0.0001, odds ratio=1.34) shows that countries with high employ rates are 1.34 times more likely to have female employ rates of 50%+. There is 95% confidence that the likelihood falls between 1.2 and 1.49.
The results support my original hypthesis of the inverse but significant relationship between the female employ rate and the urban rate.


SAS Code

PROC IMPORT DATAFILE="/home/mst07221/gapminder.csv"
DBMS=CSV
OUT=WORK.GAPMINDER;
GETNAMES=YES;
RUN;

******************************************************************************************
DATA MANAGEMENT
*******************************************************************************************;
*****************************************************
Parameterization of the country attribute:
0 = Africa
1 = Asia
2 = Europe
3 = North America
4 = Oceania
5 = South America
*****************************************************;
data new; set WORK.GAPMINDER;
if country = 'Algeria' then country_c = 0;
if country = 'Angola' then country_c = 0;
if country = 'Benin' then country_c = 0;
if country = 'Botswana' then country_c = 0;
if country = 'Burkina Faso' then country_c = 0;
if country = 'Burundi' then country_c = 0;
if country = 'Cameroon' then country_c = 0;
if country = 'Cape Verde' then country_c = 0;
if country = 'Central African Rep.' then country_c = 0;
if country = 'Chad' then country_c = 0;
if country = 'Comoros' then country_c = 0;
if country = 'Congo, Dem. Rep.' then country_c = 0;
if country = 'Congo, Rep.' then country_c = 0;
if country = 'Cote d''Ivoire' then country_c = 0;
if country = 'Djibouti' then country_c = 0;
if country = 'Egypt' then country_c = 0;
if country = 'Equatorial Guinea' then country_c = 0;
if country = 'Eritrea' then country_c = 0;
if country = 'Ethiopia' then country_c = 0;
if country = 'Gabon' then country_c = 0;
if country = 'Gambia' then country_c = 0;
if country = 'Ghana' then country_c = 0;
if country = 'Guinea' then country_c = 0;
if country = 'Guinea-Bissau' then country_c = 0;
if country = 'Kenya' then country_c = 0;
if country = 'Lesotho' then country_c = 0;
if country = 'Liberia' then country_c = 0;
if country = 'Libya' then country_c = 0;
if country = 'Madagascar' then country_c = 0;
if country = 'Malawi' then country_c = 0;
if country = 'Mali' then country_c = 0;
if country = 'Mauritania' then country_c = 0;
if country = 'Mauritius' then country_c = 0;
if country = 'Morocco' then country_c = 0;
if country = 'Mozambique' then country_c = 0;
if country = 'Namibia' then country_c = 0;
if country = 'Niger' then country_c = 0;
if country = 'Nigeria' then country_c = 0;
if country = 'Reunion' then country_c = 0;
if country = 'Rwanda' then country_c = 0;
if country = 'Sao Tome and Principe' then country_c = 0;
if country = 'Senegal' then country_c = 0;
if country = 'Seychelles' then country_c = 0;
if country = 'Sierra Leone' then country_c = 0;
if country = 'Somalia' then country_c = 0;
if country = 'South Africa' then country_c = 0;
if country = 'Sudan' then country_c = 0;
if country = 'Swaziland' then country_c = 0;
if country = 'Tanzania' then country_c = 0;
if country = 'Togo' then country_c = 0;
if country = 'Tunisia' then country_c = 0;
if country = 'Uganda' then country_c = 0;
if country = 'Zambia' then country_c = 0;
if country = 'Zimbabwe' then country_c = 0;
if country = 'Afghanistan' then country_c = 1;
if country = 'Bahrain' then country_c = 1;
if country = 'Bangladesh' then country_c = 1;
if country = 'Bhutan' then country_c = 1;
if country = 'Brunei' then country_c = 1;
if country = 'Cambodia' then country_c = 1;
if country = 'China' then country_c = 1;
if country = 'Guam' then country_c = 1;
if country = 'Hong Kong, China' then country_c = 1;
if country = 'India' then country_c = 1;
if country = 'Indonesia' then country_c = 1;
if country = 'Iran' then country_c = 1;
if country = 'Iraq' then country_c = 1;
if country = 'Israel' then country_c = 1;
if country = 'Japan' then country_c = 1;
if country = 'Jordan' then country_c = 1;
if country = 'Kazakhstan' then country_c = 1;
if country = 'Korea, Dem. Rep.' then country_c = 1;
if country = 'Korea, Rep.' then country_c = 1;
if country = 'Kuwait' then country_c = 1;
if country = 'Kyrgyzstan' then country_c = 1;
if country = 'Laos' then country_c = 1;
if country = 'Lebanon' then country_c = 1;
if country = 'Macao, China' then country_c = 1;
if country = 'Malaysia' then country_c = 1;
if country = 'Maldives' then country_c = 1;
if country = 'Mongolia' then country_c = 1;
if country = 'Myanmar' then country_c = 1;
if country = 'Nepal' then country_c = 1;
if country = 'Oman' then country_c = 1;
if country = 'Pakistan' then country_c = 1;
if country = 'Philippines' then country_c = 1;
if country = 'Qatar' then country_c = 1;
if country = 'Russia' then country_c = 1;
if country = 'Saudi Arabia' then country_c = 1;
if country = 'Singapore' then country_c = 1;
if country = 'Sri Lanka' then country_c = 1;
if country = 'Syria' then country_c = 1;
if country = 'Taiwan' then country_c = 1;
if country = 'Tajikistan' then country_c = 1;
if country = 'Thailand' then country_c = 1;
if country = 'Timor-Leste' then country_c = 1;
if country = 'Turkey' then country_c = 1;
if country = 'Turkmenistan' then country_c = 1;
if country = 'United Arab Emirates' then country_c = 1;
if country = 'Uzbekistan' then country_c = 1;
if country = 'Vietnam' then country_c = 1;
if country = 'West Bank and Gaza' then country_c = 1;
if country = 'Yemen, Rep.' then country_c = 1;
if country = 'Albania' then country_c = 2;
if country = 'Andorra' then country_c = 2;
if country = 'Armenia' then country_c = 2;
if country = 'Austria' then country_c = 2;
if country = 'Azerbaijan' then country_c = 2;
if country = 'Belarus' then country_c = 2;
if country = 'Belgium' then country_c = 2;
if country = 'Bosnia and Herzegovina' then country_c = 2;
if country = 'Bulgaria' then country_c = 2;
if country = 'Croatia' then country_c = 2;
if country = 'Cyprus' then country_c = 2;
if country = 'Czech Rep.' then country_c = 2;
if country = 'Denmark' then country_c = 2;
if country = 'Estonia' then country_c = 2;
if country = 'Faeroe Islands' then country_c = 2;
if country = 'Finland' then country_c = 2;
if country = 'France' then country_c = 2;
if country = 'Georgia' then country_c = 2;
if country = 'Germany' then country_c = 2;
if country = 'Gibraltar' then country_c = 2;
if country = 'Greece' then country_c = 2;
if country = 'Hungary' then country_c = 2;
if country = 'Iceland' then country_c = 2;
if country = 'Ireland' then country_c = 2;
if country = 'Italy' then country_c = 2;
if country = 'Latvia' then country_c = 2;
if country = 'Liechtenstein' then country_c = 2;
if country = 'Lithuania' then country_c = 2;
if country = 'Luxembourg' then country_c = 2;
if country = 'Macedonia, FYR' then country_c = 2;
if country = 'Malta' then country_c = 2;
if country = 'Moldova' then country_c = 2;
if country = 'Monaco' then country_c = 2;
if country = 'Montenegro' then country_c = 2;
if country = 'Netherlands' then country_c = 2;
if country = 'Norway' then country_c = 2;
if country = 'Poland' then country_c = 2;
if country = 'Portugal' then country_c = 2;
if country = 'Romania' then country_c = 2;
if country = 'San Marino' then country_c = 2;
if country = 'Serbia' then country_c = 2;
if country = 'Serbia and Montenegro' then country_c = 2;
if country = 'Slovak Republic' then country_c = 2;
if country = 'Slovenia' then country_c = 2;
if country = 'Spain' then country_c = 2;
if country = 'Sweden' then country_c = 2;
if country = 'Switzerland' then country_c = 2;
if country = 'Ukraine' then country_c = 2;
if country = 'United Kingdom' then country_c = 2;
if country = 'Antigua and Barbuda' then country_c = 3;
if country = 'Aruba' then country_c = 3;
if country = 'Bahamas' then country_c = 3;
if country = 'Barbados' then country_c = 3;
if country = 'Belize' then country_c = 3;
if country = 'Bermuda' then country_c = 3;
if country = 'Canada' then country_c = 3;
if country = 'Cayman Islands' then country_c = 3;
if country = 'Cook Islands' then country_c = 3;
if country = 'Costa Rica' then country_c = 3;
if country = 'Cuba' then country_c = 3;
if country = 'Dominica' then country_c = 3;
if country = 'Dominican Rep.' then country_c = 3;
if country = 'El Salvador' then country_c = 3;
if country = 'Greenland' then country_c = 3;
if country = 'Grenada' then country_c = 3;
if country = 'Guadeloupe' then country_c = 3;
if country = 'Guatemala' then country_c = 3;
if country = 'Haiti' then country_c = 3;
if country = 'Honduras' then country_c = 3;
if country = 'Jamaica' then country_c = 3;
if country = 'Martinique' then country_c = 3;
if country = 'Mexico' then country_c = 3;
if country = 'Netherlands Antilles' then country_c = 3;
if country = 'Nicaragua' then country_c = 3;
if country = 'Panama' then country_c = 3;
if country = 'Puerto Rico' then country_c = 3;
if country = 'Saint Kitts and Nevis' then country_c = 3;
if country = 'Saint Lucia' then country_c = 3;
if country = 'Saint Vincent and the Grenadines' then country_c = 3;
if country = 'Trinidad and Tobago' then country_c = 3;
if country = 'United States' then country_c = 3;
if country = 'Australia' then country_c = 4;
if country = 'Fiji' then country_c = 4;
if country = 'French Polynesia' then country_c = 4;
if country = 'Kiribati' then country_c = 4;
if country = 'Marshall Islands' then country_c = 4;
if country = 'Micronesia, Fed. Sts.' then country_c = 4;
if country = 'Nauru' then country_c = 4;
if country = 'New Caledonia' then country_c = 4;
if country = 'New Zealand' then country_c = 4;
if country = 'Niue' then country_c = 4;
if country = 'Palau' then country_c = 4;
if country = 'Papua New Guinea' then country_c = 4;
if country = 'Samoa' then country_c = 4;
if country = 'Solomon Islands' then country_c = 4;
if country = 'Tonga' then country_c = 4;
if country = 'Tuvalu' then country_c = 4;
if country = 'Vanuatu' then country_c = 4;
if country = 'Argentina' then country_c = 5;
if country = 'Bolivia' then country_c = 5;
if country = 'Brazil' then country_c = 5;
if country = 'Chile' then country_c = 5;
if country = 'Colombia' then country_c = 5;
if country = 'Ecuador' then country_c = 5;
if country = 'Guyana' then country_c = 5;
if country = 'Paraguay' then country_c = 5;
if country = 'Peru' then country_c = 5;
if country = 'Suriname' then country_c = 5;
if country = 'Uruguay' then country_c = 5;
if country = 'Venezuela' then country_c = 5;

**make the quantitative response variable a binary variable
** split the female employment rate to above(1)/below(0) 50%;
if femaleemployrate < 50 then fememploy = 0;
else fememploy = 1;

run;

**************************************************************************************
END DATA MANAGEMENT
**************************************************************************************;

**************************************************************************************
CATEGORICAL EXPLANATORY VARIABLES RE-VISITED (3+ CATEGORIES)
***************************************************************************************;
* centering quantitative explanatory variables; 
* print mean;
PROC MEANS;
var femaleemployrate urbanrate incomeperperson internetuserate polityscore lifeexpectancy employrate;
run;

PROC GLM; 
model femaleemployrate=urbanrate incomeperperson internetuserate polityscore lifeexpectancy employrate/solution;
run;

* centering (subtract mean);
data new2;
set new;
urbanrate_c = urbanrate - 56.7693596;
incomeperperson_c = incomeperperson - 8740.97;
internetuserate_c = internetuserate - 35.6327158;
polityscore_c = polityscore - 3.6894410;
lifeexpectancy_c = lifeexpectancy - 69.7535236;
employrate_c = employrate - 58.6359551;
run;

* check coding;
PROC MEANS;
var urbanrate_c incomeperperson_c internetuserate_c polityscore_c lifeexpectancy_c employrate_c;
run;

** simple linear regression modelling;
PROC GLM; 
model femaleemployrate=urbanrate_c incomeperperson_c internetuserate_c polityscore_c lifeexpectancy_c employrate_c/solution;
run;

*Reference group = countries in Africa;
PROC GLM; 
class country_c (ref="0"); 
model femaleemployrate=urbanrate_c incomeperperson_c internaeeserate_c polityscore_c
 lifeexpectancy_c employrate_ccountry_c/solution;
run;

* Reference group = countries in Asia;
PROC GLM; 
class  country_c (ref="1"); 
model femaleemployrate=urbanrate_c incomeperperson_c internaeeserate_c polityscore_c
 lifeexpectancy_c employrate_ccountry_c/solution;
run;

* Reference group = countries in Europe;
PROC GLM; 
class  country_c (ref="2"); 
model femaleemployrate=urbanrate_c incomeperperson_c internaeeserate_c polityscore_c
 lifeexpectancy_c employrate_ccountry_c/solution;
run;

* Reference group = countries in North America;
PROC GLM; 
class  country_c (ref="3"); 
model femaleemployrate=urbanrate_c incomeperperson_c internaeeserate_c polityscore_c
 lifeexpectancy_c employrate_ccountry_c/solution;
run;

* Reference group = countries in Oceania;
PROC GLM; 
class  country_c (ref="4"); 
model femaleemployrate=urbanrate_c incomeperperson_c internaeeserate_c polityscore_c
 lifeexpectancy_c employrate_ccountry_c/solution;
run;

* Reference group = countries in South America;
PROC GLM; 
class  country_c (ref="5"); 
model femaleemployrate=urbanrate_c incomeperperson_c internaeeserate_c polityscore_c
 lifeexpectancy_c employrate_ccountry_c/solution;
run;

*****************************************************************************************
LOGISTIC REGRESSION
*****************************************************************************************;
Proc logistic descending; 
model  fememploy=  urbanrate;_c
run;

Proc logistic descending; 
model  fememploy=  urbanrate_c; incomeperperson_c
run;

Proc logistic descending; 
modee  fememploy= urbanrate _c incomeperperson_c internetuserate_c
run;

PProc logistic descending; 
model  fememploy= urbanrate_c incomeperperson_c internetuserate_c polityscore_c;
run;

Proc logistic descending; 
model  fememploy= urbanrate_c incomeperperson_c internetuserate_c polityscore_c;
run;

Proc logistic descending; 
model  fememploy= urbanrate_c incomeperperson_c internetuserate_c polityscore_c lifeexpectancy_c;
run;

Proc logistic descending; 
model  fememploy= urbanrate_c incomeperperson_c internetuserate_c polityscore_c lifeexpectancy_c employrate_c;
run;

Results
The MEANS Procedure



VariableNMeanStd DevMinimumMaximum
femaleemployrate
urbanrate
incomeperperson
internetuserate
polityscore
lifeexpectancy
employrate
178
203
190
192
161
191
178
47.5494381
56.7693596
8740.97
35.6327158
3.6894410
69.7535236
58.6359551
14.6257425
23.8449326
14262.81
27.7802846
6.3148991
9.7086205
10.5194545
11.3000002
10.4000000
103.7758572
0.2100663
-10.0000000
47.7940000
32.0000000
83.3000031
100.0000000
105147.44
95.6381132
10.0000000
83.3940000
83.1999969

The GLM Procedure
Number of Observations Read213
Number of Observations Used150

The GLM Procedure
Dependent Variable: femaleemployrate
SourceDFSum of SquaresMean SquareF ValuePr > F
Model625581.913344263.6522287.46<.0001
Error1436971.2965948.75033
Corrected Total14932553.20994
R-SquareCoeff VarRoot MSEfemaleemployrate Mean
0.78584914.515696.98214348.10067
SourceDFType I SSMean SquareF ValuePr > F
urbanrate14068.928664068.9286683.46<.0001
incomeperperson11806.332391806.3323937.05<.0001
internetuserate118.8495718.849570.390.5351
polityscore1196.33302196.333024.030.0467
lifeexpectancy11716.203131716.2031335.20<.0001
employrate117775.2665717775.26657364.62<.0001
SourceDFType III SSMean SquareF ValuePr > F
urbanrate1161.04308161.043083.300.0712
incomeperperson156.3689956.368991.160.2840
internetuserate1398.94589398.945898.180.0049
polityscore1835.38354835.3835417.14<.0001
lifeexpectancy1284.70984284.709845.840.0169
employrate117775.2665717775.26657364.62<.0001
ParameterEstimateStandard
Error
t ValuePr > |t|
Intercept-8.3949785857.72729710-1.090.2791
urbanrate-0.0693920590.03817926-1.820.0712
incomeperperson-0.0001124920.00010461-1.080.2840
internetuserate0.1322797490.046240782.860.0049
polityscore0.4115901330.099428474.14<.0001
lifeexpectancy-0.2331244410.09646624-2.420.0169
employrate1.2021325270.0629554119.09<.0001

The MEANS Procedure
VariableNMeanStd DevMinimumMaximum
urbanrate_c
incomeperperson_c
internetuserate_c
polityscore_c
lifeexpectancy_c
employrate_c
203
190
192
161
191
178
5.9113279E-9
-0.0039237
-3.097827E-8
-6.211181E-9
-3.979057E-8
-1.810316E-8
23.8449326
14262.81
27.7802846
6.3148991
9.7086205
10.5194545
-46.3693596
-8637.19
-35.4226495
-13.6894410
-21.9595236
-26.6359551
43.2306404
96406.47
60.0053974
6.3105590
13.6404764
24.5640418

The GLM Procedure
Number of Observations Read213
Number of Observations Used150

The GLM Procedure
Dependent Variable: femaleemployrate
SourceDFSum of SquaresMean SquareF ValuePr > F
Model625581.913344263.6522287.46<.0001
Error1436971.2965948.75033
Corrected Total14932553.20994
R-SquareCoeff VarRoot MSEfemaleemployrate Mean
0.78584914.515696.98214348.10067
SourceDFType I SSMean SquareF ValuePr > F
urbanrate_c14068.928664068.9286683.46<.0001
incomeperperson_c11806.332391806.3323937.05<.0001
internetuserate_c118.8495718.849570.390.5351
polityscore_c1196.33302196.333024.030.0467
lifeexpectancy_c11716.203131716.2031335.20<.0001
employrate_c117775.2665717775.26657364.62<.0001
SourceDFType III SSMean SquareF ValuePr > F
urbanrate_c1161.04308161.043083.300.0712
incomeperperson_c156.3689956.368991.160.2840
internetuserate_c1398.94589398.945898.180.0049
polityscore_c1835.38354835.3835417.14<.0001
lifeexpectancy_c1284.70984284.709845.840.0169
employrate_c117775.2665717775.26657364.62<.0001
ParameterEstimateStandard
Error
t ValuePr > |t|
Intercept47.141347160.5882981880.13<.0001
urbanrate_c-0.069392060.03817926-1.820.0712
incomeperperson_c-0.000112490.00010461-1.080.2840
internetuserate_c0.132279750.046240782.860.0049
polityscore_c0.411590130.099428474.14<.0001
lifeexpectancy_c-0.233124440.09646624-2.420.0169
employrate_c1.202132530.0629554119.09<.0001

The GLM Procedure
Class Level Information
ClassLevelsValues
country_c61 2 3 4 5 0
Number of Observations Read213
Number of Observations Used148

The GLM Procedure
Dependent Variable: femaleemployrate
SourceDFSum of SquaresMean SquareF ValuePr > F
Model1126988.924922453.5386363.82<.0001
Error1365228.5022538.44487
Corrected Total14732217.42717
R-SquareCoeff VarRoot MSEfemaleemployrate Mean
0.83771212.897706.20039348.07365
SourceDFType I SSMean SquareF ValuePr > F
urbanrate_c13885.570813885.57081101.07<.0001
incomeperperson_c11885.430201885.4302049.04<.0001
internetuserate_c18.399978.399970.220.6409
polityscore_c1161.21451161.214514.190.0425
lifeexpectancy_c11624.642811624.6428142.26<.0001
employrate_c118435.2334918435.23349479.52<.0001
country_c5988.43314197.686635.140.0002
SourceDFType III SSMean SquareF ValuePr > F
urbanrate_c125.0707725.070770.650.4208
incomeperperson_c17.924547.924540.210.6505
internetuserate_c118.4558118.455810.480.4896
polityscore_c1216.34246216.342465.630.0191
lifeexpectancy_c1108.05325108.053252.810.0959
employrate_c117361.3315817361.33158451.59<.0001
country_c5988.43314197.686635.140.0002
ParameterEstimateStandard
Error
t ValuePr > |t|
Intercept45.51220706B1.4669149031.03<.0001
urbanrate_c-0.030518350.03779169-0.810.4208
incomeperperson_c-0.000045070.00009926-0.450.6505
internetuserate_c0.033579760.048465220.690.4896
polityscore_c0.239909810.101133802.370.0191
lifeexpectancy_c-0.197906750.11804861-1.680.0959
employrate_c1.290683720.0607361921.25<.0001
country_c 1-0.65423435B1.90496373-0.340.7318
country_c 27.96674783B2.493181243.200.0017
country_c 3-1.55741061B2.54395495-0.610.5414
country_c 41.90130435B3.283769330.580.5635
country_c 50.74774921B2.824272320.260.7916
country_c 00.00000000B...
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.

The GLM Procedure
Class Level Information
ClassLevelsValues
country_c60 2 3 4 5 1
Number of Observations Read213
Number of Observations Used148

The GLM Procedure
Dependent Variable: femaleemployrate
SourceDFSum of SquaresMean SquareF ValuePr > F
Model1126988.924922453.5386363.82<.0001
Error1365228.5022538.44487
Corrected Total14732217.42717
R-SquareCoeff VarRoot MSEfemaleemployrate Mean
0.83771212.897706.20039348.07365
SourceDFType I SSMean SquareF ValuePr > F
urbanrate_c13885.570813885.57081101.07<.0001
incomeperperson_c11885.430201885.4302049.04<.0001
internetuserate_c18.399978.399970.220.6409
polityscore_c1161.21451161.214514.190.0425
lifeexpectancy_c11624.642811624.6428142.26<.0001
employrate_c118435.2334918435.23349479.52<.0001
country_c5988.43314197.686635.140.0002
SourceDFType III SSMean SquareF ValuePr > F
urbanrate_c125.0707725.070770.650.4208
incomeperperson_c17.924547.924540.210.6505
internetuserate_c118.4558118.455810.480.4896
polityscore_c1216.34246216.342465.630.0191
lifeexpectancy_c1108.05325108.053252.810.0959
employrate_c117361.3315817361.33158451.59<.0001
country_c5988.43314197.686635.140.0002
ParameterEstimateStandard
Error
t ValuePr > |t|
Intercept44.85797271B1.1170497640.16<.0001
urbanrate_c-0.030518350.03779169-0.810.4208
incomeperperson_c-0.000045070.00009926-0.450.6505
internetuserate_c0.033579760.048465220.690.4896
polityscore_c0.239909810.101133802.370.0191
lifeexpectancy_c-0.197906750.11804861-1.680.0959
employrate_c1.290683720.0607361921.25<.0001
country_c 00.65423435B1.904963730.340.7318
country_c 28.62098218B1.904724224.53<.0001
country_c 3-0.90317626B2.10153887-0.430.6680
country_c 42.55553870B3.016570310.850.3984
country_c 51.40198356B2.464500080.570.5704
country_c 10.00000000B...
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.

The GLM Procedure
Class Level Information
ClassLevelsValues
country_c60 1 3 4 5 2
Number of Observations Read213
Number of Observations Used148

The GLM Procedure
Dependent Variable: femaleemployrate
SourceDFSum of SquaresMean SquareF ValuePr > F
Model1126988.924922453.5386363.82<.0001
Error1365228.5022538.44487
Corrected Total14732217.42717
R-SquareCoeff VarRoot MSEfemaleemployrate Mean
0.83771212.897706.20039348.07365
SourceDFType I SSMean SquareF ValuePr > F
urbanrate_c13885.570813885.57081101.07<.0001
incomeperperson_c11885.430201885.4302049.04<.0001
internetuserate_c18.399978.399970.220.6409
polityscore_c1161.21451161.214514.190.0425
lifeexpectancy_c11624.642811624.6428142.26<.0001
employrate_c118435.2334918435.23349479.52<.0001
country_c5988.43314197.686635.140.0002
SourceDFType III SSMean SquareF ValuePr > F
urbanrate_c125.0707725.070770.650.4208
incomeperperson_c17.924547.924540.210.6505
internetuserate_c118.4558118.455810.480.4896
polityscore_c1216.34246216.342465.630.0191
lifeexpectancy_c1108.05325108.053252.810.0959
employrate_c117361.3315817361.33158451.59<.0001
country_c5988.43314197.686635.140.0002
ParameterEstimateStandard
Error
t ValuePr > |t|
Intercept53.47895489B1.4640955636.53<.0001
urbanrate_c-0.030518350.03779169-0.810.4208
incomeperperson_c-0.000045070.00009926-0.450.6505
internetuserate_c0.033579760.048465220.690.4896
polityscore_c0.239909810.101133802.370.0191
lifeexpectancy_c-0.197906750.11804861-1.680.0959
employrate_c1.290683720.0607361921.25<.0001
country_c 0-7.96674783B2.49318124-3.200.0017
country_c 1-8.62098218B1.90472422-4.53<.0001
country_c 3-9.52415844B2.25625098-4.22<.0001
country_c 4-6.06544348B3.12448527-1.940.0543
country_c 5-7.21899862B2.59052312-2.790.0061
country_c 20.00000000B...
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.

The GLM Procedure
Class Level Information
ClassLevelsValues
country_c60 1 2 4 5 3
Number of Observations Read213
Number of Observations Used148

The GLM Procedure
Dependent Variable: femaleemployrate
SourceDFSum of SquaresMean SquareF ValuePr > F
Model1126988.924922453.5386363.82<.0001
Error1365228.5022538.44487
Corrected Total14732217.42717
R-SquareCoeff VarRoot MSEfemaleemployrate Mean
0.83771212.897706.20039348.07365
SourceDFType I SSMean SquareF ValuePr > F
urbanrate_c13885.570813885.57081101.07<.0001
incomeperperson_c11885.430201885.4302049.04<.0001
internetuserate_c18.399978.399970.220.6409
polityscore_c1161.21451161.214514.190.0425
lifeexpectancy_c11624.642811624.6428142.26<.0001
employrate_c118435.2334918435.23349479.52<.0001
country_c5988.43314197.686635.140.0002
SourceDFType III SSMean SquareF ValuePr > F
urbanrate_c125.0707725.070770.650.4208
incomeperperson_c17.924547.924540.210.6505
internetuserate_c118.4558118.455810.480.4896
polityscore_c1216.34246216.342465.630.0191
lifeexpectancy_c1108.05325108.053252.810.0959
employrate_c117361.3315817361.33158451.59<.0001
country_c5988.43314197.686635.140.0002
ParameterEstimateStandard
Error
t ValuePr > |t|
Intercept43.95479645B1.8281262224.04<.0001
urbanrate_c-0.030518350.03779169-0.810.4208
incomeperperson_c-0.000045070.00009926-0.450.6505
internetuserate_c0.033579760.048465220.690.4896
polityscore_c0.239909810.101133802.370.0191
lifeexpectancy_c-0.197906750.11804861-1.680.0959
employrate_c1.290683720.0607361921.25<.0001
country_c 01.55741061B2.543954950.610.5414
country_c 10.90317626B2.101538870.430.6680
country_c 29.52415844B2.256250984.22<.0001
country_c 43.45871496B3.270915791.060.2922
country_c 52.30515982B2.621036640.880.3807
country_c 30.00000000B...
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.

The GLM Procedure
Class Level Information
ClassLevelsValues
country_c60 1 2 3 5 4
Number of Observations Read213
Number of Observations Used148

The GLM Procedure
Dependent Variable: femaleemployrate
SourceDFSum of SquaresMean SquareF ValuePr > F
Model1126988.924922453.5386363.82<.0001
Error1365228.5022538.44487
Corrected Total14732217.42717
R-SquareCoeff VarRoot MSEfemaleemployrate Mean
0.83771212.897706.20039348.07365
SourceDFType I SSMean SquareF ValuePr > F
urbanrate_c13885.570813885.57081101.07<.0001
incomeperperson_c11885.430201885.4302049.04<.0001
internetuserate_c18.399978.399970.220.6409
polityscore_c1161.21451161.214514.190.0425
lifeexpectancy_c11624.642811624.6428142.26<.0001
employrate_c118435.2334918435.23349479.52<.0001
country_c5988.43314197.686635.140.0002
SourceDFType III SSMean SquareF ValuePr > F
urbanrate_c125.0707725.070770.650.4208
incomeperperson_c17.924547.924540.210.6505
internetuserate_c118.4558118.455810.480.4896
polityscore_c1216.34246216.342465.630.0191
lifeexpectancy_c1108.05325108.053252.810.0959
employrate_c117361.3315817361.33158451.59<.0001
country_c5988.43314197.686635.140.0002
ParameterEstimateStandard
Error
t ValuePr > |t|
Intercept47.41351142B2.8239275516.79<.0001
urbanrate_c-0.030518350.03779169-0.810.4208
incomeperperson_c-0.000045070.00009926-0.450.6505
internetuserate_c0.033579760.048465220.690.4896
polityscore_c0.239909810.101133802.370.0191
lifeexpectancy_c-0.197906750.11804861-1.680.0959
employrate_c1.290683720.0607361921.25<.0001
country_c 0-1.90130435B3.28376933-0.580.5635
country_c 1-2.55553870B3.01657031-0.850.3984
country_c 26.06544348B3.124485271.940.0543
country_c 3-3.45871496B3.27091579-1.060.2922
country_c 5-1.15355514B3.50164499-0.330.7423
country_c 40.00000000B...
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.

The GLM Procedure
Class Level Information
ClassLevelsValues
country_c60 1 2 3 4 5
Number of Observations Read213
Number of Observations Used148

The GLM Procedure
Dependent Variable: femaleemployrate
SourceDFSum of SquaresMean SquareF ValuePr > F
Model1126988.924922453.5386363.82<.0001
Error1365228.5022538.44487
Corrected Total14732217.42717
R-SquareCoeff VarRoot MSEfemaleemployrate Mean
0.83771212.897706.20039348.07365
SourceDFType I SSMean SquareF ValuePr > F
urbanrate_c13885.570813885.57081101.07<.0001
incomeperperson_c11885.430201885.4302049.04<.0001
internetuserate_c18.399978.399970.220.6409
polityscore_c1161.21451161.214514.190.0425
lifeexpectancy_c11624.642811624.6428142.26<.0001
employrate_c118435.2334918435.23349479.52<.0001
country_c5988.43314197.686635.140.0002
SourceDFType III SSMean SquareF ValuePr > F
urbanrate_c125.0707725.070770.650.4208
incomeperperson_c17.924547.924540.210.6505
internetuserate_c118.4558118.455810.480.4896
polityscore_c1216.34246216.342465.630.0191
lifeexpectancy_c1108.05325108.053252.810.0959
employrate_c117361.3315817361.33158451.59<.0001
country_c5988.43314197.686635.140.0002
ParameterEstimateStandard
Error
t ValuePr > |t|
Intercept46.25995627B2.2207895920.83<.0001
urbanrate_c-0.030518350.03779169-0.810.4208
incomeperperson_c-0.000045070.00009926-0.450.6505
internetuserate_c0.033579760.048465220.690.4896
polityscore_c0.239909810.101133802.370.0191
lifeexpectancy_c-0.197906750.11804861-1.680.0959
employrate_c1.290683720.0607361921.25<.0001
country_c 0-0.74774921B2.82427232-0.260.7916
country_c 1-1.40198356B2.46450008-0.570.5704
country_c 27.21899862B2.590523122.790.0061
country_c 3-2.30515982B2.62103664-0.880.3807
country_c 41.15355514B3.501644990.330.7423
country_c 50.00000000B...
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.

The LOGISTIC Procedure
Model Information
Data SetWORK.NEW2
Response Variablefememploy
Number of Response Levels2
Modelbinary logit
Optimization TechniqueFisher's scoring
Number of Observations Read213
Number of Observations Used203
Response Profile
Ordered
Value
fememployTotal
Frequency
1176
20127
Probability modeled is fememploy=1.
Note:10 observations were deleted due to missing values for the response or explanatory variables.
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
CriterionIntercept OnlyIntercept and Covariates
AIC270.467265.476
SC273.780272.102
-2 Log L268.467261.476
Testing Global Null Hypothesis: BETA=0
TestChi-SquareDFPr > ChiSq
Likelihood Ratio6.990810.0082
Score6.909610.0086
Wald6.738910.0094
Analysis of Maximum Likelihood Estimates
ParameterDFEstimateStandard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept1-0.53220.148312.88720.0003
urbanrate_c1-0.01640.006326.73890.0094
Odds Ratio Estimates
EffectPoint Estimate95% Wald
Confidence Limits
urbanrate_c0.9840.9720.996
Association of Predicted Probabilities and Observed Responses
Percent Concordant60.5Somers' D0.211
Percent Discordant39.4Gamma0.211
Percent Tied0.1Tau-a0.099
Pairs9652c0.605

The LOGISTIC Procedure
Model Information
Data SetWORK.NEW2
Response Variablefememploy
Number of Response Levels2
Modelbinary logit
Optimization TechniqueFisher's scoring
Number of Observations Read213
Number of Observations Used189
Response Profile
Ordered
Value
fememployTotal
Frequency
1173
20116
Probability modeled is fememploy=1.
Note:24 observations were deleted due to missing values for the response or explanatory variables.
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
CriterionIntercept OnlyIntercept and Covariates
AIC254.140251.476
SC257.382261.201
-2 Log L252.140245.476
Testing Global Null Hypothesis: BETA=0
TestChi-SquareDFPr > ChiSq
Likelihood Ratio6.664520.0357
Score6.614520.0366
Wald6.300620.0428
Analysis of Maximum Likelihood Estimates
ParameterDFEstimateStandard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept1-0.48640.152710.14060.0015
urbanrate_c1-0.01910.007626.27330.0123
incomeperperson_c10.0000150.0000131.38820.2387
Odds Ratio Estimates
EffectPoint Estimate95% Wald
Confidence Limits
urbanrate_c0.9810.9670.996
incomeperperson_c1.0001.0001.000
Association of Predicted Probabilities and Observed Responses
Percent Concordant61.8Somers' D0.235
Percent Discordant38.2Gamma0.235
Percent Tied0.0Tau-a0.112
Pairs8468c0.618

The LOGISTIC Procedure
Model Information
Data SetWORK.NEW2
Response Variablefememploy
Number of Response Levels2
Modelbinary logit
Optimization TechniqueFisher's scoring
Number of Observations Read213
Number of Observations Used182
Response Profile
Ordered
Value
fememployTotal
Frequency
1172
20110
Probability modeled is fememploy=1.
Note:31 observations were deleted due to missing values for the response or explanatory variables.
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
CriterionIntercept OnlyIntercept and Covariates
AIC246.313244.655
SC249.517257.471
-2 Log L244.313236.655
Testing Global Null Hypothesis: BETA=0
TestChi-SquareDFPr > ChiSq
Likelihood Ratio7.657530.0536
Score7.402530.0601
Wald6.716730.0815
Analysis of Maximum Likelihood Estimates
ParameterDFEstimateStandard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept1-0.43520.15557.83260.0051
urbanrate_c1-0.01660.008793.55310.0594
incomeperperson_c10.0000380.0000213.10570.0780
internetuserate_c1-0.008860.009580.85640.3548
Odds Ratio Estimates
EffectPoint Estimate95% Wald
Confidence Limits
urbanrate_c0.9840.9671.001
incomeperperson_c1.0001.0001.000
internetuserate_c0.9910.9731.010
Association of Predicted Probabilities and Observed Responses
Percent Concordant65.5Somers' D0.310
Percent Discordant34.5Gamma0.310
Percent Tied0.0Tau-a0.149
Pairs7920c0.655

The LOGISTIC Procedure
Model Information
Data SetWORK.NEW2
Response Variablefememploy
Number of Response Levels2
Modelbinary logit
Optimization TechniqueFisher's scoring
Number of Observations Read213
Number of Observations Used153
Response Profile
Ordered
Value
fememployTotal
Frequency
1166
2087
Probability modeled is fememploy=1.
Note:60 observations were deleted due to missing values for the response or explanatory variables.
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
CriterionIntercept OnlyIntercept and Covariates
AIC211.212198.007
SC214.242213.159
-2 Log L209.212188.007
Testing Global Null Hypothesis: BETA=0
TestChi-SquareDFPr > ChiSq
Likelihood Ratio21.204340.0003
Score20.248540.0004
Wald18.251340.0011
Analysis of Maximum Likelihood Estimates
ParameterDFEstimateStandard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept1-0.21350.17991.40860.2353
urbanrate_c1-0.03800.011311.32020.0008
incomeperperson_c10.0000930.0000328.23930.0041
internetuserate_c1-0.01210.01270.90500.3414
polityscore_c1-0.004250.03020.01980.8880
Odds Ratio Estimates
EffectPoint Estimate95% Wald
Confidence Limits
urbanrate_c0.9630.9420.984
incomeperperson_c1.0001.0001.000
internetuserate_c0.9880.9641.013
polityscore_c0.9960.9391.056
Association of Predicted Probabilities and Observed Responses
Percent Concordant71.5Somers' D0.429
Percent Discordant28.5Gamma0.429
Percent Tied0.0Tau-a0.212
Pairs5742c0.715

The LOGISTIC Procedure
Model Information
Data SetWORK.NEW2
Response Variablefememploy
Number of Response Levels2
Modelbinary logit
Optimization TechniqueFisher's scoring
Number of Observations Read213
Number of Observations Used153
Response Profile
Ordered
Value
fememployTotal
Frequency
1166
2087
Probability modeled is fememploy=1.
Note:60 observations were deleted due to missing values for the response or explanatory variables.
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
CriterionIntercept OnlyIntercept and Covariates
AIC211.212198.007
SC214.242213.159
-2 Log L209.212188.007
Testing Global Null Hypothesis: BETA=0
TestChi-SquareDFPr > ChiSq
Likelihood Ratio21.204340.0003
Score20.248540.0004
Wald18.251340.0011
Analysis of Maximum Likelihood Estimates
ParameterDFEstimateStandard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept1-0.21350.17991.40860.2353
urbanrate_c1-0.03800.011311.32020.0008
incomeperperson_c10.0000930.0000328.23930.0041
internetuserate_c1-0.01210.01270.90500.3414
polityscore_c1-0.004250.03020.01980.8880
Odds Ratio Estimates
EffectPoint Estimate95% Wald
Confidence Limits
urbanrate_c0.9630.9420.984
incomeperperson_c1.0001.0001.000
internetuserate_c0.9880.9641.013
polityscore_c0.9960.9391.056
Association of Predicted Probabilities and Observed Responses
Percent Concordant71.5Somers' D0.429
Percent Discordant28.5Gamma0.429
Percent Tied0.0Tau-a0.212
Pairs5742c0.715

The LOGISTIC Procedure
Model Information
Data SetWORK.NEW2
Response Variablefememploy
Number of Response Levels2
Modelbinary logit
Optimization TechniqueFisher's scoring
Number of Observations Read213
Number of Observations Used153
Response Profile
Ordered
Value
fememployTotal
Frequency
1166
2087
Probability modeled is fememploy=1.
Note:60 observations were deleted due to missing values for the response or explanatory variables.
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
CriterionIntercept OnlyIntercept and Covariates
AIC211.212196.396
SC214.242214.579
-2 Log L209.212184.396
Testing Global Null Hypothesis: BETA=0
TestChi-SquareDFPr > ChiSq
Likelihood Ratio24.815350.0002
Score23.643550.0003
Wald21.003850.0008
Analysis of Maximum Likelihood Estimates
ParameterDFEstimateStandard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept1-0.22080.18221.46840.2256
urbanrate_c1-0.03330.01168.22160.0041
incomeperperson_c10.0000880.0000327.60190.0058
internetuserate_c10.001540.01460.01110.9159
polityscore_c1-0.000400.03090.00020.9897
lifeexpectancy_c1-0.05490.02943.49850.0614
Odds Ratio Estimates
EffectPoint Estimate95% Wald
Confidence Limits
urbanrate_c0.9670.9460.990
incomeperperson_c1.0001.0001.000
internetuserate_c1.0020.9731.031
polityscore_c1.0000.9411.062
lifeexpectancy_c0.9470.8941.003
Association of Predicted Probabilities and Observed Responses
Percent Concordant73.0Somers' D0.459
Percent Discordant27.0Gamma0.459
Percent Tied0.0Tau-a0.227
Pairs5742c0.730

The LOGISTIC Procedure
Model Information
Data SetWORK.NEW2
Response Variablefememploy
Number of Response Levels2
Modelbinary logit
Optimization TechniqueFisher's scoring
Number of Observations Read213
Number of Observations Used150
Response Profile
Ordered
Value
fememployTotal
Frequency
1166
2084
Probability modeled is fememploy=1.
Note:63 observations were deleted due to missing values for the response or explanatory variables.
Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
CriterionIntercept OnlyIntercept and Covariates
AIC207.779122.260
SC210.790143.334
-2 Log L205.779108.260
Testing Global Null Hypothesis: BETA=0
TestChi-SquareDFPr > ChiSq
Likelihood Ratio97.51936<.0001
Score69.85466<.0001
Wald33.87886<.0001
Analysis of Maximum Likelihood Estimates
ParameterDFEstimateStandard
Error
Wald
Chi-Square
Pr > ChiSq
Intercept1-0.63300.26495.70950.0169
urbanrate_c1-0.01710.01561.19350.2746
incomeperperson_c14.544E-60.0000390.01340.9077
internetuserate_c10.02130.01911.24620.2643
polityscore_c10.04880.04851.01170.3145
lifeexpectancy_c1-0.02230.04370.26070.6097
employrate_c10.29240.054328.9439<.0001
Odds Ratio Estimates
EffectPoint Estimate95% Wald
Confidence Limits
urbanrate_c0.9830.9531.014
incomeperperson_c1.0001.0001.000
internetuserate_c1.0220.9841.060
polityscore_c1.0500.9551.155
lifeexpectancy_c0.9780.8981.065
employrate_c1.3401.2041.490
Association of Predicted Probabilities and Observed Responses
Percent Concordant92.4Somers' D0.848
Percent Discordant7.6Gamma0.848
Percent Tied0.0Tau-a0.421
Pairs5544c0.924