Log.27

A lasso regression analysis was conducted to identify a subset of variables from a pool of 14 quantitative predictor variables that best predicted a quantitative response variable measuring income per person among countries. Quantitative predictor variables include alcconsumption, armedforcesrate,  breastcancerper100th, co2emissions, femaleemployrate, hivrate, internetuserate, lifeexpectancy, oilperperson, polityscore, relectricperperson, suicideper100th, employrate, and urbanrate. 

Data were randomly split into a training set that included 70% of the observations (N=40) and a test set that included 30% of the observations (N=16). The least angle regression algorithm with k=10 fold cross validation was used to estimate the lasso regression model in the training set, and the model was validated using the test set. The change in the cross validation average (mean) squared error at each step was used to identify the best subset of predictor variables.

I selected the variables from data set Gapminder. The binary categorical response variable is internet use rate, a quantitative variable collapsed into 2 categories. If internet use rate >=50%，then Internet use rate _ adjusted = 1; if f internet use rate <50%，then Internet use rate _ adjusted = 0.  The explanatory variables are all quantitative variables, including income per person, polity score, female employment rate, life expectancy, employment rate, urbanization rate alcohol consumption and suicide per 100th.

My research question is whether individuals who drank at least 1 alcoholic drink in last 12 months is associated with his or her blood/natural father ever an alcoholic or problem drinker . The categorical response variable is s2aq3, “drank at least 1 alcoholic drink in last 12 months”, “1″ represent “yes” and “0″ represent “no”; the categorical explanatory variable is s2dq1, “blood/natural father is ever an alcoholic or problem drinker”,  “1″ represent “yes” and “0″ represent “no” . in addition, majordeplife, major depression, is a potential confounding variable.

By conducting logistic regression model, as shown in the tables above, p-value for s2dq1 is less than 0.0001, indicating “ blood/natural father is ever an alcoholic or problem drinker” is significantly associated with individual who “ drank at least 1 alcoholic drink in last 12 months” . The odds ratio is 1.337, which means that individuals whose fathers are drinkers are more likely (1.337 times) have at least 1 alcoholic drink in last 12 months more than those whose fathers are not drinkers. The odds ratio illustrates the comparison in terms of probability. The confidence interval is  [1.270, 1.408], so we are 95% confident that the population odds ratio will fall between 1.270 and 1.408. The confidence interval excludes 1, which also proves that the relationship is significant.

The testing result supports my hypothesis that individuals who drank at least 1 alcoholic drink in last 12 months is associated with his or her blood/natural father ever an alcoholic or problem drinker. i make the hypothesis since  i believed the behaviour of parents would affect the behaviour of children.

An additional logistic regression model is conducted to test confounding variable. after adding the major depression variable into the model, since the p-value of s2dq1 remains less than 0.0001, indicating statistical significance. I conclude that major depression is not a confounding variable. The Odd ratios becomes 1.295, which means that individuals whose fathers are drinkers are more likely (1.295 times) have at least 1 alcoholic drink in last 12 months more than those whose fathers are not drinkers. the odds ratio illustrates the comparison in terms of probability. The confidence interval is  [1.229, 1.365], so we are 95% confident that the population odds ratio will fall between 1.229 and 1.365. the confidence interval excludes 1, which also proves that the relationship is significant.

My research question is the association between Urbanization Rate and Employment rate. My quantitative response variable is Employment Rate, while my quantitative explanatory variable is Urbanization Rate. The potential confounding variable is Polity Score.

By processing GLM procedure, the tables above shows that both Urbanization Rate and the square of Urbanization Rate are statistically correlated with Employment Rate. The Urbanization Rate and the square of Urbanization Rate have P-values less than 0.0001, which are definitely less than the level of significance, 0.05. In other words, the null hypothesis is rejected.  In addition, the beta coefficients are  -0.15460947 and 0.00608523 respectively. The r-square is  0.207473, indicating that roughly 21% of the employment rate can be explained by the variables in the model.

The result supports my hypothesis that the employment rate is associated with urbanization rate.

The GLM procedure is also conducted to test whether the polity score is a confounder, affecting the relationship between the response variable and explanatory variable. The table above shows that P-value for polity score is as large as  0.3430, while P value for urbanization rate and P vale for the square of Urbanization rate keep very small.  As a result, polity score is not a confounding variable.

To better characterize the model, several  regression diagnostic plots are generated.

Q-Q plot: Some points are deviated from the line, indicating the residuals are not perfectly normally distributed. This is a evidence that the model should include some other explanatory variables. As a result, the model does not fit best.

Standardized residuals for all observations:  If the residuals are normally distributed, about 95 percent of points should lie within plus and minus two units of standard deviations. According to the graph, there are 10 points out of the line, since only 152 observations used, 142/152=0.9342=93.42%. Therefore, the standard is probably not met.

The decision tree analysis (classification tree in this case) is conducted to test non-linear relationship among the binary response variable (alcevr1, alcohol use) , the categorical explanatory variables and quantitative explanatory variables.

The explanatory variables included in this model are listed as following: age, gender, (race/ethnicity) Hispanic, White, Black, Native American and Asian, alcohol problem, marijuana use, cocaine use, inhalant use, availability of cigarettes in the home, whether or not either parent was on public assistance, any experience with being expelled from school. alcohol problems, deviance, violence, depression, self-esteem, parental presence, parental activities, family connectedness, school connectedness and grade point average (GPA).

The research question is whether the female employ rate is associated with life expectancy.The explanatory variable “female employ rate” is quantitative variables. A linear regression model is tested to identify the relationship between them.

As the model shows, F-statistic equals 13.98 and P value is 0.0003, which is far less than the level of statistical significance 0.05. It indicates that female employ rate is statistically significantly correlated with life expectancy.

The mean procedure is conducted to center the mean to 0. 

As the original mean table shows, the original mean of female employ rate is about 47.549. The Variable “femaleemployrate_centered” is modified to reflect the adjustment. As the new mean table shows, the means of female employ rate is very closed to zero.

The table also shows an intercept of 69.556 with a slope of -0.1853. The best-fit line can be interpreted as,

lifeexpectancy = 69.556 - 0.1853 * femaleemployrate_centered.  

R-square = 0.074382, 

My Assignment is correlation coefficient test that includes a moderator is showed as below,

The moderator is income group. I classify income of each country into 4 income group. 

If Income <= 10000, then income group 1

If Income > 10000 and <=20000, then income group 2 

If Income > 20000 and <=30000, then income group 3 

If income > 30000, then income group 4

In situation of income group 1, the r value between alcconsumption(alcohol consumption) and internetuserate(internet use rate) is 0.58786,indicate a positive linear relationship.  It is neither strong nor weak linear relationship. Since p value is 0.0001, the relationship is statistically significant. Finally, Since r x r = 0.58786 x 0.58786 = 0.3455793796, if we know the “internetuserate(internet use rate)”, we can predict approximately 34.56% of the variability we will see in the rate of alcconsumption(alcohol consumption). This means that approximately 65.44% of the variability is unaccounted for. 

In situation of income group 2, the r value between alcconsumption(alcohol consumption) and internetuserate(internet use rate) is 0.31017, Since p value is 0.2423 >0.05, the relationship is NOT statistically significant.

In situation of income group 3, the r value between alcconsumption(alcohol consumption) and internetuserate(internet use rate) is 0.26647,Since p value is 0.3789 >0.05, the relationship is NOT statistically significant.

SAS code is showed as below,

The result is showed as below,

(1) The r value between alcconsumption(alcohol consumption) and internetuserate(internet use rate) is 0.53448, indicate a positive linear relationship. It is neither strong nor weak linear relationship. Since p value is 0.0001, the relationship is statistically significant. Finally, Since r x r = 0.53448 x 0.53448 = 0.2856688704, if we know the “internetuserate(internet use rate)”, we can predict 29% of the variability we will see in the rate of alcconsumption(alcohol consumption). This means that 71% of the variability is unaccounted for.

66.LIBNAME mydata "/courses/d1406ae5ba27fe300 " access=readonly; DATA new; SET mydata.gapminder; /*data management for income per person*/ if incomeperperson <=10000 then ipp="1"; if incomeperperson > 10000 and incomeperperson <=20000 then ipp="2"; if incomeperperson >20000 and incomeperperson <=30000 then ipp="3"; if incomeperperson >30000 then ipp="4"; /*data management for female employ rate*/ if femaleemployrate <=50 then fer=0; if femaleemployrate >50 then fer=1; PROC SORT; by COUNTRY; PROC FREQ; TABLES fer*ipp/CHISQ; RUN; DATA COMPARISON1; SET NEW; IF ipp=1 OR ipp=2; PROC SORT; BY COUNTRY; PROC FREQ; TABLES fer*ipp/CHISQ; RUN; DATA COMPARISON2; SET NEW; IF ipp=1 OR ipp=3; PROC SORT; BY COUNTRY; PROC FREQ; TABLES fer*ipp/CHISQ; RUN; DATA COMPARISON3; SET NEW; IF ipp=1 OR ipp=4; PROC SORT; BY COUNTRY; PROC FREQ; TABLES fer*ipp/CHISQ; RUN; DATA COMPARISON4; SET NEW; IF ipp=2 OR ipp=3; PROC SORT; BY COUNTRY; PROC FREQ; TABLES fer*ipp/CHISQ; RUN; DATA COMPARISON5; SET NEW; IF ipp=2 OR ipp=4; PROC SORT; BY COUNTRY; PROC FREQ; TABLES fer*ipp/CHISQ; RUN; DATA COMPARISON6; SET NEW; IF ipp=3 OR ipp=4; PROC SORT; BY COUNTRY; PROC FREQ; TABLES fer*ipp/CHISQ; RUN;

SAS OUTPUT DATA

Since Gapminder dateset is all quantitative explanatory variable, I categorized quantitative explanatory variable to categorical explanatory variable. I also categorized quantitative response variable to categorical response variable. My null hypothesis is income per person(ipp) is not associated with female employ rate(fer). Alter hypothesis is income per person(ipp) is associated with female employ rate(fer).

As showed in the first table,

If fer=0 which means female employ rate <=50%,

ipp(income per person) between 0 to $10,000 is 66.87%.

ipp(income per person) between 0 to $10,000 is 64.71%. 

ipp(income per person) between 0 to $10,000 is 57.14%. 

ipp(income per person) between 0 to $10,000 is 43.75%.

if fer=1 which means female employ rate >50%,

ipp(income per person) between 0 to $10,000 is 33.13%.

ipp(income per person) between 0 to $10,000 is 35.29%.

ipp(income per person) between 0 to $10,000 is 42.86%.

ipp(income per person) between 0 to $10,000 is 56.25%.

In total, p-value is 0.2916>0.05, fail to reject null hypothesis.

In comparison 1 , p-value is 0.8571/6=0.14285>0.05, fail to reject null hypothesis.

In comparison 2 , p-value is 0.4604/6=0.077>0.05,fail to reject null hypothesis.

In comparison 3 , p-value is 0.0644/6=0.011<0.05,reject null hypothesis.

In comparison 4 , p-value is 0.6670/6=0.111>0.05, fail to reject null hypothesis.

In comparison 5 , p-value is 0.2269/6=0.0378<0.05,reject null hypothesis.

The SAS coding and results provided as below link

https://www.dropbox.com/sh/1cvfk176oviffhl/AACZuVg52LN6ZleBU9xXh1m5a?dl=0

The null hypothesis is that there is no statistically significant difference between the female employ rate among polity score of each country. The alternate hypothesis is that there is a statistically significant difference.

Model Interpretation for ANOVA:

When examining the association between female employ rate (quantitative response) and polity score of each country (categorical explanatory), an Analysis of Variance (ANOVA) indicated that there are 21 levels, 158 data used out of 213.Since P value is 0.0680 greater than significant level value 0.05. Hence, I concluded fail to reject the null hypothesis. The polity score doesn’t affect female employee rate in each country.

Model Interpretation for post hoc ANOVA results:

Sample

The sample is from the program “GapMinder” founded in Stockholm by Ola Rosling, Anna Rosling Ronnlund and Hans Rosling, it is a non-profit venture promoting sustainable global development and achievement of the United Nations Millennium Development Goals. It seeks to increase the use and understanding of statistics about social economic, and environmental development at local, national, and global levels. My selected sample focus on the association between “Income per person” and “Female employment rate”, “Internet use rates”. Participants ( N= 213) represented the countries in the world. It includes 15 observations. Specifically, “income per person”, “alcohol consumption per adult”, “Armed forces personnel”, “2006 cumulative CO2 emission”, “2007 total employees age 15+”, “2009 estimated HIV Prevalence %”, “2010 Internet users”, “2011 life expectancy at birth”, “2010 oil Consumption per capita”, “2009 Democracy score”, “2008 residential electricity consumption, per person”, “2005 Suicide, age adjusted”, “2008 urban population”. I only selected two observations, “Female employment rate” and “Internet use rates” to be my data analytic sample in order to analysis the association with income per person.

Procedure

The original purpose of the data collection is to increase the use and understanding of statistics about social economic, and environmental development at local, national, and global levels. Data were come from a handful of sources, including the Institute for Health Metrics and Evaluation, US Census Bureau’s International Database, United Nations Statistics Division, and the World Bank. In 2005, Gapminder has grown to include over 200 indicators, including gross domestic product, total employment rate, and estimated HIV prevalence. Gapminder contains data for all 192 UN members, aggregating data for Serbia and Montenegro. Additionally, it includes data for 24 other areas, generating a total of 215 areas.

Measures

SUMMARY

(1)   The first graph is unimodal, with its highest peak at the category of $0 to $2000 income per person. It seems to be skewed to the right as there are higher frequencies in lower categories than the higher categories.

(2)    The second graph is unimodal, with its highest peak at the category of 40% to 60% female employ rate. It seems to be skewed to the right as there are higher frequencies in lower categories than the higher categories.

(3)   The third graph is unimodal, with its highest peak at the category of 0% to 20% internet use rate. It seems to be skewed to the right as there are higher frequencies in lower categories than the higher categories.

I put week 2 Assignment in dropbox. Please check it. 

I chose three variable like “income per person”,”female employ rate”,”internet use rates”. Each row represent each country.  I also set condition to check how many frequency that personal income below $2000; how many frequency that female employ rate below 50%, and how many frequency that internet use rate below 50%. 

In order to compare, i also upload the ORIGINAL output table WITHOUG CONDITION in the dropbox.

1) There are 34 countrys that “income per person” with condition below $2000 (with 17 frequency missing). There are 190 countries without condition below $2000(with 23 frequency missing). Therefore, 17.89% country that “ income per person” below $2000.

2) There are 41 countrys that “female employment rate” with condition below 50% (with 17 frequency missing). There are 178 country without condition below 50%.(with 35 frequency missing). Therefore, 23.03% country that “female employment rate” below 50%.

(1) I picked “Gapminder data files (.csv)” as my research data set.

(2)

a)  Research question: Is female employ rate associated with GDP?

b)  My hypothesis: Does GDP positively relative with female employ rate?

(3)

a)  Second research topic: Is Internet use rate associated with GDP?

b)  My hypothesis: Does GPD positively relative with Internet use rate?

(4)

literature review: I found some previous research had been done in this topic. There is a research “The Impact of Broadband on the Economy” mentioned that broadband penetration does contribute to GPD growth. The research confirms the contribution to GDP growth but the amount of impact varies widely. It indicated GDP growing evidence of increasing returns to broadband penetration. Therefore, I am sure Internet use rate will be a variable associate with GDP. I also believe Internet use rate positive relatively with GDP.