sabah t rahman

When I think of photography, I often think of Anaïs Nin’s quote, “We don’t see things as they are; we see them as we are.” Translated within the context of photography, I relate to the sentiment that ‘how’ we see the world is also influenced by ‘who’ we are. To talk about what defines my photography, I have to talk about Meena, my childhood feminist ‘shero.’  

Meena is a creation of UNICEF Bangladesh in the 1990’s to celebrate the decade of the girl child. It quickly became one of my favourite cartoons growing up. Meena’s stories involved her adventures in her colourful village with her younger brother, Raju, and their talking pet parrot, Mithu.  

Led by the nine-year-old Meena, the short, animated films would involve the trio taking on social issues in their small community, including the rights of children to education, health, protection, development and participate in decisions that impacted their lives.  

As a little girl growing up in Bangladesh, Meena was my role model! Meena spoke Bangla, and I was drawn to her tenacity, sunny disposition, and intelligence. Mostly, I admired how Meena navigated society’s expectations from young women.  

From early on, I learned to see conventions not as immutable, rather that, which could be influenced or changed. I wanted to study photojournalism and documentary photography at Loyalist College in Ontario to visually craft stories of the world I inhabit. Being a visual documentarian allows me to engage the world around me creatively and investigate social issues I often wonder about.

One of the photographers I have studied closely is Dorothea Lange, and looking at her body of work, I admire the honesty in her images, her empathy for those whom she was photographing and her portrayal of human resilience. Lange’s photography is defined by the timeless quality of examining the human condition. This is something that inspires me, that I try to emulate in my own work.  

SAS syntax to test logit models

LIBNAME mydata "/courses/d1406ae5ba27fe300 " access=readonly; data new; set mydata.gapminder;

if urbanrate ne . and internetuserate ne . and polityscore ne .; /* setting aside missing data */

if polityscore > -6 and polityscore < 6 then regtype=0; /* anocracy */ if polityscore  >= 6 then regtype=1; /* democracy; also reference group */

/* CENTRING THE MEAN */ proc means; var urbanrate internetuserate; /* means procedure to find the mean for centring var's */ data new2; set new; /* creating a new dataset new2 */ urbanrate_ctrd=urbanrate-55.3735484; /* quan exp var 1; creating new variable by centring the mean */ intuserate_ctrd=internetuserate-32.5309464; /* quan exp var 2; creating new variable be centring the mean */ proc means; var urbanrate_ctrd intuserate_ctrd; /* means procedure to validate centring */

/* LOGISTIC REGRESSION MODELS */ proc logistic descending; model regtype=urbanrate_ctrd; /* testing assc'n with urbanization */ proc logistic descending; model regtype=intuserate_ctrd; /* testing assc'n with internet use rate */ proc logistic descending; model regtype=urbanrate_ctrd intuserate_ctrd; /* testing for confounding variable */

run;

Output

PROC MEANS to centre explanatory variables and checking new variables:

Logit model to test any association with quantitative explanatory variable #1 or urbanization:

Logit model to test association with quantitative explanatory variable #2 or internet use rate:

Logit model testing for confounding effects on associations and including both explanatory variables (e.g., urbanization and internet use rate):

Interpretation

This week, I am testing a logistic regression model based on a binary categorical response variable ‘polity score’ from the Polity IV dataset, and quantitative explanatory variables ‘internet use rate’ (2010) and ‘urbanization’ (2008) from the World Bank data available in Gapminder. 

In my data management steps, I have created a new variable “regtype” by categorizing countries with polity scores between -5 and 5 (or, anocracy regime type) as zero “0″, and countries with polity scores between 6 and 10 (or, democracy regime type) as one “1″. The PROC LOGISTIC descending procedure tested for the association between the categorical response variable (i.e., regtype) and quantitative explanatory variables (i.e., urbanrate_ctrd & intuserate_ctrd) where there is a presence of democracy. Note that the “descending” code in PROC LOGISTIC step tells SAS to denote regtype=1 as the presence of democracy and regtype=0 (or anocracy regime category) as its absence.    

The key research question is: What happens to the odds of the presence of democracy when we account for urbanization and internet use rates in a sample of countries? 

I am setting up three separate models to answer my question, that is I am checking for the association of each explanatory variables with the categorical response variable (i.e., regtype-urbanrate_ctrd, and regtype-intuserate_ctrd) and one model that tests for confounding effects by including both explanatory variables (i.e., regtype-urbanrate_ctrd & intuserate_ctrd).

My hypothesis is that both explanatory variables are significantly associated with the categorical response variable (even after testing for confounding effects), and value(s) of the explanatory variable(s) increase(s) since the odds of the presence of democracy is more likely; in other words, I expect the odds ratio in each test to be greater than 1. 

Instead of looking for true expected values (as in a multiple linear regression model where response variable is quantitative), I am looking for “the probability of an event occuring” (i.e., odds ratio) as the response variable is categorical and can only take on the values 0 and 1. Since my explanatory variables are both quantitative (as opposed to being categorical), the odds ratios will show what happens to the odds of the presence of democracy in a sample with every one unit increase in explanatory variable(s).

(i) For association with quantitative explanatory variable #1, i.e., urbanrate_ctrd: 

The results show that the odds ratio estimate is 1.031 and the  p-value is significant at 0.0005. The results may be interpreted to say that there is a significant association in this relationship, and with every one unit increase in urbanization rate, the odds of the presence of democracy increases in likelihood by 1.031% in the sample. The confidence ratio shows that we can be 95% confident that if we selected another sample from the population and ran the same tests, the odds of the presence of democracy will increase somewhere between 1.014% and 1.050% with every one unit increase in urbanization rate within the sample.

(ii) For association with quantitative explanatory variable #2, i.e, intuserate_ctrd:

The results show that the odds ratio estimate is 1.058 and the p-value is significant at less than .0001. So, there is a positive association between internet use rate and the presence of democracy. With every one unit increase in internet use rate, the likelihood of the odds of the presence of democracy in the sample increases by 1.058%. In a new sample of the population this increase in the odds of the presence of democracy will be somewhere between 1.034% and 1.082% about ninety-five times out of a hundred trials if the same tests were also run. 

(iii) For association with both urbanrate_ctrd and intuserate_ctrd explanatory variables:

When we account for internet use rate in the model, urbanization is no longer significantly associated with the presence of democracy (p-value is 0.3995, much higher than the alpha of 0.05). So, there is evidence of confounding when we control for internet use rate in the model. The p-value for internet use rate is still significant and less than .0001. We may interpret the results to say that the odds of the presence of democracy increases by 1.066% with every unit increase in internet use rate, when we also account for urbanization rate in the model. The 95% Wald Confidence Limits tell us that the odds of the presence of democracy is somewhere between 1.035% and 1.098% about ninety-five times out of a hundred trials if another sample was drawn from the population and the same test was run. 

(iv) Summary conclusion and hypothesis testing:

SAS syntax to test a multiple linear regression model and generate various regression diagnostic plots

LIBNAME mydata "/courses/d1406ae5ba27fe300 " access=readonly; data new; set mydata.gapminder; if urbanrate ne . and internetuserate ne . and polityscore ne .;

/* SCATTERPLOT LINEAR & QUADRATIC REGRESSION LINE */ proc sgplot; reg x=polityscore y=internetuserate / lineattrs=(color=blue thickness=1) degree=1 clm; /* 1st order polynomial or a linear line */ reg x=polityscore y=internetuserate / lineattrs=(color=green thickness=1) degree=2 clm; /* 2nd order polynomial or a qudratic line */ xaxis label="Polity score"; yaxis label="Internet use rate (per 100 people)";

/* CENTRING THE MEAN */ proc means; var urbanrate; /* means procedure to find the mean */ data new2; set new; /* creating a new dataset new2 */ urbanrate_ctrd=urbanrate-55.3735484; /* quan exp var 2; creating new variable by centring the mean */ proc means; var urbanrate_ctrd; /* means procedure to validate centring */

/* LINEAR REGRESSION MODEL - E.G. COMPARISON OF BEST FIT TO VALIDATE */ proc glm; model internetuserate=polityscore/solution clparm; proc glm; model internetuserate=polityscore polityscore*polityscore/solution clparm; /* adding quadratic term = polityscore2 */

/* MULTIPLE LINEAR REGRESSION MODEL AND REGRESSION DIAGNOSTIC PLOTS */   proc glm plots (unpack)=all; model internetuserate=polityscore polityscore*polityscore urbanrate_ctrd/solution clparm; output residual=res student=stdres out=results;

/* REGRESSION DIAGNOSTIC PLOTS: STANDARDIZED RESIDUAL PLOT */ proc gplot; label stdres="Standardized Residual" country="Country"; plot stdres*country/vref=0 1 2 -1 -2;

run;

Output

Scatterplot with linear and quadratic regression line; response variable (y axis) is internet use rate and primary explanatory variable (x axis) is Polity score

PROC MEANS output for urbanrate and urbanrate_ctrd (secondary explanatory variable)

Linear regression model between internet use rate and polity score - comparison to validate best fit model

Adding quadratic term polityscore-squared - comparison to validate best fit model

Multiple linear regression model - adding quadratic term and urbanrate explanatory variable 

Regression diagnostic plots; e.g., q-q plot

Regression diagnostic plots, e.g., standardized residual plot

Regression diagnostic plots, e.g., leverage plot

Interpretation

Looking back to the visualizations and analysis I created for internet use rate and polity score in the previous courses of this specialization, my hypothesis for this week’s regression analysis is that (i) there is a positive association between internet use rate and polity score after controlling for other explanatory variables, and (ii) a quadratic line will likely be a better fit for this model as internet use rate spikes at both extremes of the policy scores or the two opposing regime type categories (i.e., democracy and autocracy).   

I began my analysis with a scatterplot where I asked SAS to generate a linear and quadratic regression line between the association of internet use rate and polity score (primary explanatory variable). The scatterplot shows us that the quadratic regression line better explains the association between internet use rate and polity score, which is evidently curvilinear; whereas, the points are really far away from the straight line of the linear regression line,  meaning there would be a lot of prediction error if this model was used for further analysis. The quadratic regression line captures the association between internet use rate and polity score at two ends, and in the case the countries that are democratic (with scores GE 6) and autocratic (with score LE -6). The points, or the expected / predicted values, at these levels are much closer to the observed values for the quadratic regression line. 

Although I centred the urbanrate explanatory variable, as the polityscore already has a value of zero (for anocracy regime type countries), this variable was not centred for further analysis.

To see which model is a better fit, I tested the GLM procedure with and without the quadratic terms to validate my assumptions between the association of internet use rate and polityscore as my primary explanatory variable and urbanrate_ctrd as my secondary explanatory variable:

The linear regression model between internet use rate and polity score shows that there is a positive association as I had predicted. However, the regression coefficient value is  1.60425078 and this model only predicts 13% of the variability in the predicted internet use rate. The confidence intervals show that the true population parameters fall somewhere between 0.95 and 2.26.

After adding the quadratic term or the squared-polityscore and the centred urbanrate explanatory variable, the output shows that after controlling for the quadratic term of polityscore and urbanrate_ctrd, there is no longer a significant association between the primary explanatory variable polityscore and internet use rate. This indicates confounding effects within the model on the primary explanatory variable after controlling for other variables. Additionally, the added explanatory variables significantly improves the variability of predicting internet use rate (up to 63%). There are significant associations in the model (p value for both quadratic term of polityscore and urbanrate_ctrd is <.0001). All three explanatory variables have positive parameter estimates, although the values are quite low for every one unit increase in x. The confidence interval show that the range of the parameter estimates for the quadratic term of polityscore is between 0.24 and 0.45, and between 0.44 and 0.7 for urbanrate_ctrd.   

The better fit model shows that the null hypothesis is true (that is, no association) in the association between polityscore and internet use rate after controlling for the quadratic term of polityscore and urbanrate_ctrd as additional explanatory variables in the multiple linear regression model. 

The q-q plot evaluates the assumption that the residuals in our model are normally distributed, and it plots the quantiles of the residuals that we would theoretically see if the residuals followed a normal distribution (that is, against the quantiles for the residuals estimated from our resssion model). The q-q plot above shows that the residuals are not normally distributed and do not follow a straight line especially toward the higher and the lower quantiles. This also indicates that the curvilinear association may require additional explanatory variables, in addition to the quadratic term and the urbanrate_ctrd explanatory variable that was used. 

The standardized residual plot shows the overall fit of the response variable to the observed values and specific outliers. The standardized residuals transform the residual values to have a mean of zero and a standard deviation of 1, and this is done to standardize or normalize the values so they fit a standard normal distribution. The plot above shows that most of the variables fall within 2+/- standard deviations from the mean, and there are no extreme outliers. The plot indicates the overall fit of the model, the distribution of the residuals and the level of error are within acceptable limits, as less than 5% of the values are within 2+/- standard deviations of the mean and none of the values exceeded 2.5+/- standard deviations from the mean. 

SAS syntax to test a basic linear regression model

LIBNAME mydata "/courses/d1406ae5ba27fe300 " access=readonly; data new; set mydata.gapminder; label internetuserate="Internet use rate" urbanrate="Urban population";

/* DATA MANAGEMENT */ if polityscore GE 6; /* subsetting dataset to only include democracy regime category countries */ if urbanrate ne . and internetuserate ne .; /* setting aside missing data */ urbanrate_ctrd=urbanrate-59.6938636; /* quan exp var; centring the mean=0 or close to zero */ proc means; var urbanrate; /* means procedure */ proc means; var urbanrate_ctrd; /* means procedure to validate */

/* SCATTERPLOT LINEAR REGRESSION LINE */ proc sgplot; reg x=urbanrate y=internetuserate; xaxis label="Urban population (% of total)"; yaxis label="Internet use rate (per 100 people)";

/* LINEAR REGRESSION MODEL */ proc glm; model internetuserate=urbanrate_ctrd/solution;

run;

Output

Means procedure for explanatory variable “urbanrate” and “urbanrate_ctrd” where the mean=0 or close to zero

Scatterplot graph with linear regression line

GLM procedure

Interpretation

Using the Gapminder dataset, I am testing a basic linear regression model for the association between my primary quantitative explanatory variable (i.e., urbanization rate) and a response variable (i.e., internet use rate).

To start off, I have subset my data to include only the sample of countries which belong to democracy regime type based on the Polity IV dataset within Gapminder. In my data management steps, I have also accounted for missing data within the dataset.

Since I am using a quantitative explanatory variable, in this case the urbanization rate, for my linear regression model, I have centred the mean so that it equals to zero or close to zero. The mean was also calculated using the means procedure in SAS to check the centring step. 

Using the PROC GLM procedure, I analyzed the data within the framework of general linear models and used it to test my basic linear regression model on the correlation between number of internet users and urbanization rate. To recap, the first goal was to determine the equation of the best fit line between the two variables:

y = ß0 + ß1x where, - y represents the response variable - ß0 represnts population y intercept - ß1 represents population slope coefficient - x represents the explanatory variable 

In this case, the equation of the best fit line of this scatterplot of the linear regression line is:

internetuserate = 42.48 +  0.91 * urbanrate

The number of observations with complete data that was used in this model is 88. The F statistic is 74.59 and the Pr > F is <.0001, both of which are significant and show that there is a signficant relationship between internet use rate and urbanization. Additionally, the Pr > |t| gives us the p value for the explanatory variable’s association with the response variable, which is <.0001 and it is the same value we would get if a pearson correlation was also run. 

Sample 

The Polity IV dataset covers all major, independent states in the global system over the period 1800-2014 (i.e., states with a total population of 500,000 or more in the most recent year; currently 167 countries). 

The Polity scheme consists of six component measures that record key qualities of of executive recruitment, constraints on executive authority and political competition. It also records changes in the institutionalized qualities of governing authority. 

The Polity data include information only on the institutions of the central government and on political groups acting, or reacting, within the scope of that authority. (Note: it does not include consideration of groups and territories that are actively removed from that authority or segments of the population that are not yet effectively politicized in relation to central state politics.) 

I have included the whole sample in my analysis, but have noted the distinct groupings based on regime categories within the sample.   

Procedure 

The Polity IV dataset is the fourth of the series and improves on various analytical techniques since Polity I dataset was first introduced in 1970′s. Originally, the project was meant to measure political system durability but have since broadened to encompass regime types more generally, including a measure of the degree of democracy and autocracy.  

The dataset includes ordinal-scale indicators that are based on expert coding on subjective interpretation of real-time events to make tentative assessments of the trajectories of unfolding political dynamics and their effect on the essential qualities of governing institutions, or patterns of authority. Recent annual Polity records are routinely reexamined during each annual update and may be revised in light of further information regarding institutional practice.    

The "Polity Score" captures this regime authority spectrum on a 21-point scale ranging from -10 (hereditary monarchy) to +10 (consolidated democracy). The Polity scores can also be converted into regime categories in a suggested three part categorization of "autocracies" (-10 to -6), "anocracies" (-5 to +5 and three special values: -66, -77 and -88), and "democracies" (+6 to +10). The Polity score is computed by subtracting the Autocracy score from the Democracy score; the resulting unified polity scale ranges from +10 (strongly democratic) to -10 (strongly autocratic). 

The project is currently under the direction of Monty G. Marshall at the Center for Systemic Peace and George Mason University.

Measure

For my analysis on any associations between internet usage and regime type categories (Polity IV dataset), I introduced another variable on residential electricity consumption per person.

Internet users (per 100 people) 2010 dataset is based on the World Development Indicator by the World Bank which measures the number of individuals per 100 people who have access to the worldwide network.  

Residential electricity consumption per person measures the amount of residential electricity consumption per person during the given year, counted in kilowatt-hours (kWh). This dataset was made available in the Gapminder website based on the World Energy Outlook 2010 by the International Energy Agency. 

My analysis included three distinct groupings of countries or regime categories that are based on the assigned Polity scores in the Polity IV dataset. I also used the binning technique to classify high (i.e., >50) versus low (i.e., <50) levels, for both internet users and residential electricity consumption rates.  

1. SAS syntax

LIBNAME mydata "/courses/d1406ae5ba27fe300 " access=readonly; data new; set mydata.gapminder;

/* data management polityscore */ if polityscore <= -6 then regtype="Autocracy"; if polityscore > -6 and polityscore < 6 then regtype="Anocracy"; if polityscore  >= 6 then regtype="Democracy";

/* data management residential electricity consumption */ if relectricperperson < 50 then reselec="Low"; if relectricperperson >= 50 then reselec="High";

/* data management internet use */ if internetuserate < 50 then intuser="Low"; if internetuserate >= 50 then intuser="High";

/* ANOVA F test */ proc sort; by regtype; proc anova; class reselec; model internetuserate=reselec; means reselec; by regtype;

/* chi square test of independence */ proc sort; by regtype; proc freq; tables intuser*reselec/chisq; by regtype;

/* pearson correlation coefficient test */ proc sort; by regtype; proc corr; var relectricperperson internetuserate; by regtype;

run;

2. Corresponding output

(a) Output of testing moderation of the categorical third variable regime type(s) (i.e. Anocracy, Autocracy, Democracy) with residential electricity consumption and no. of internet users, in the context of ANOVA

(i) Anocracy 

F and p values:

Boxplot:

(ii) Autocracy 

F and p values:

Boxplot:

(iii) Democracy

F and p values:

Boxplot:

( b )  Output of testing moderation of the categorical third variable regime type(s) (i.e. Anocracy, Autocracy, Democracy) with residential electricity consumption and no. of internet users, in the context of chi square test of independence

(i) Anocracy

(ii) Autocracy

(iii) Democracy

( c )  Output of testing moderation of the categorical third variable regime type(s) (i.e. Anocracy, Autocracy, Democracy) with residential electricity consumption and no. of internet users, in the context of pearson correlation

(i) Anocracy

(ii) Autocracy

(iii) Democracy

3. Interpretation

This week, I am attempting to find if the categorical explanatory variable (e.g. rate of residential electricity consumption - high vs. low) is associated with the quantitative response variable (e.g. no. of internet users) across each population sub-group or each level of the third categorical variable (e.g. regime type of countries, or anocracy / autocracy / democracy).  

Key question: Does the regime type category affect the strength or the direction of the association between residential electricity consumption and no. of internet users?

Null hypothesis is that the regime type category does not affect the strength or the direction of the association between residential electricity consumption and no. of internet users. 

( a ) Testing moderation in the context of ANOVA 

Countries that are in the anocracy (15.93) and the democracy (27.95) groups show large F values, and significantly associated p values (anocracy 0.0002; democracy <.0001). Countries, within anocratic and democratic regime type categories, that have high residential electricity consumption rates, have much higher mean no. of internet users, compared to the lower mean no. of internet users in countries (within the same regime type categories) that have low rates of residential electricity consumption rates. 

On the other hand, countries that are in the autocracy group, show a small F-value (0.37) and the p-value is not significant (0.5458). The mean no. of internet users are very close to each other (high 45.29; low 41.11) between high and low residential electricity consumption categories (i.e. high vs. low).

In summary:

The regime type categories anocracy and democracy are similar in how and where the mean no. of internet users appear across high and low residential electricity consuming countries. 

The mean no. of internet users in high residential electricity consuming countries is much higher for democracy regime type category, than the mean no. of internet users in high residential electricity consuming countries for anocracy regime type category. 

In fact, the overall mean no. of internet users (in high residential electricity consuming countries) for democracy regime type is more than twice the value observed for the mean no. of internet users (in high residential electricity consuming countries) for anocracy regime type.

A similar statement can also be made for the mean no. of internet users observed for low residential electricity consuming countries among democracy regime type and anocracy regime type categories. 

The mean no. of internet users among autocratic regime type category countries are very close / similar among those that have high residential electricity consumption rates and those that have low residential electricity consumption rates.

The regime type category affects the association between the variables, when comparing the no. of internet users across high and low residential electricity consuming countries, only for democracy and anocracy regime type categories, with significantly higher mean no. of internet users for democracies. The autocracy regime type category is an exception to this finding, and does not affect the association between no. of internet users and rates of residential electricity consumption.    

( b ) Testing moderation in the context of chi square test of independence 

Anocracy and autocracy regime type categories have low chi square values (anocracy 0.9396; autocracy 2.1181), and the p-values are not significant in the association between residential electricity consumption and no. of internet users (anocracy 0.3324; autocracy 0.1456). 

Democracy regime type has a low chi square value (7.3052) but the p-value is signficant in the association between residential electricity consumption and no. of internet users (0.0069).

In summary:

The rates of residential electricity consumption and no. of internet users are not significantly associated in anocracy and autocracy regime type categories (low chi square values, and p value higher than 0.05). 

50% of the cells in the chi square analysis for anocracy regime type category have expected counts less than 5, so chi-square may not be a valid test.

Column percents do not reveal a linear relationship between rates of residential electricity consumption and the no. of internet users across anocracy and autocracy regime type categories.  

The democracy regime type has a significant moderating effect in the association between residential electricity consumption and no. of internet users (p-value 0.0069), although it has a very low chi square value (7.3052); this may indicate a weaker statistically significant relationship.

( c )  Testing moderation in the context of pearson correlation

The correlation coefficients across democracy (0.73484) and anocracy (0.85310) regime types are quite high and indicate positive linear relationships, and significant p-values (democracy and anocracy p-values are both <.0001).

The correlation coefficient between residential electricity consumption and no. of internet users  has a weaker positive relationship in the autocracy regime type (0.42283), with a slightly more modest p-value (0.034) although this relationship is significant (i.e. less than 0.05). 

In summary:

The analysis of the results indicate that the correlation of rates of residential electricity consumption and no. of internet users may only slightly differ based on the regime type category.

For all three regime type categories, the association between residential electricity consumption and no. of internet users are positive linear relationships with varying degrees of strength within the relationships. 

The low p-values indicate there is a strong association between rates of residential electricity consumption and the no. of internet users among all regime type categories, although it is more modest in autocracy regime types. 

The strongest correlation (close to +1) among residential electricity consumption and no. of internet users is found among anocracy regime type category countries.

1. SAS syntax to run correlation coefficient tests between three quantitative variables from Gapminder dataset - e.g. internetuserate / relectricperperson / incomeperperson

Note that I also wanted to visually represent the association of specific quantitative variables through scatterplots. 

-----

LIBNAME mydata "/courses/d1406ae5ba27fe300 " access=readonly;

data new; set mydata.gapminder;

proc sort; by COUNTRY;

/* bivariate graph scatterplot chart - Q-->Q */ proc gplot; plot internetuserate*relectricperperson; proc gplot; plot internetuserate*incomeperperson;

/* pearson correlation coefficient test */ proc corr; var relectricperperson incomeperperson internetuserate;

run;

----

Where, the variable “internetuserate” is the number of internet users per 100 people; “relectricperperson” is the amount of residential electricity consumption per person during the given year; and, “incomeperperson” is the Gross Domestric Product per capita of countries.

2. Corresponding output 

(i) The pink highlighted boxes below highlight the association between relectricperperson and internetuserate, as well as incomeperperson and internetuserate.

(ii) Scatter plot - internetuserate and relectricperperson; note that the pattern of a relationship among two quantitative variables can be measured by the direction, form and strength of the scatter plot.  

(iii) Scatter plot - internetuserate and incomeperperson

3. Interpretation

This week I am looking at the correlation coefficient and the p-value of two sets of quantititative variables (e.g. internetuserate vs. relectricperperson, and, internetuserate vs. incomeperperson). 

The correlation coefficient measures the degree of the linear relationship between two quantitative variables, that is how a change in one variable affects a change in another variable. A correlation of +1 means that there is a perfect, positive, linear relationship between the two variables. A correlation of -1 means there is a perfect, negative linear relationship between the two variables.

By squaring the correlation coefficient value (as per the output in SAS), I can roughly guess what proportion of the variability in one variable is described by variation in the second variable. In other words, I can predict the value of one variable (e.g. internetuserate) by knowing the value of the second variable (e.g. relectricperperson). An associated p-value calculated for the correlation coefficient is significant when the p-value is less than or equal to 0.05.  

For the association between relectricperperson and internetuserate:

The correlation coefficient is 0.59 and the probability value (p-value) is <.0001

This relationship is statistically significant, and the correlation coefficient of 0.59 is more than zero (albeit, a slightly modest value in comparison) and indicates a strong positive relationship between the variables. 

The square of the correlation coefficient or  0.592 is  0.35, which indicates that by knowing the residential electricity consumption per person, counted in kilowatt-hours (kWh), I can only predict 35% of the variability of the number of internet users, per 100 people, among countries.  

The scatter plot shows a positive relationship (i.e. direction), that is an increase in relectricperperson (x-axis, explanatory variable) also results in an increase in internetuserate (y-axis, response variable). From a quick visual scan of the chart, I can roughly guess that the relationship between the two variables has a linear form (i.e. form), that is the points are dispersed along a steep-angled right-leaning line. A scan of the chart also tells me that there is likely a strong relationship (i.e. strength) between these variables.     

For the association between incomeperperson and internetuserate:

The correlation coefficient is 0.75 and the p-value is <.0001

This relationship is statistically significant, and the correlation coefficient of 0.75 is more than zero (much closer to +1, or a perfect-positive correlation) indicating a strong positive relationship between the variables.

The square of the correlation coefficient or  0.752 is  0.56, which indicates that by knowing the GDP per capita, I can predict 56% (or more than half) of the variability of the number of internet users, per 100 people, among countries. 

1. SAS syntax used to run chi square test of independence and post hoc test (i.e. Bonferroni Adjustment)

LIBNAME mydata "/courses/d1406ae5ba27fe300 " access=readonly; data new; set mydata.gapminder;

/* data management internetuserate */ if internetuserate < 50 then intuser="low"; if internetuserate >= 50 then intuser="high";

/* data management polityscore */ if polityscore <= -6 then regtype="Autocracy"; if polityscore > -6 and polityscore < 6 then regtype="Anocracy"; if polityscore  >= 6 then regtype="Democracy";

/* sorting the data by the observation, i.e. country */ proc sort; by COUNTRY;

/* chi square test of independence */ proc freq; tables intuser*regtype/chisq;

/* post hoc test for chi square test of independence, the Bonferroni Adjustment */

data comparison1; set new; if regtype="Anocracy" or regtype="Autocracy"; proc sort; by country; proc freq; tables intuser*regtype/chisq;

data comparison2; set new; if regtype="Anocracy" or regtype="Democracy"; proc sort; by country; proc freq; tables intuser*regtype/chisq;

data comparison3; set new; if regtype="Autocracy" or regtype="Democracy"; proc sort; by country; proc freq; tables intuser*regtype/chisq;

run;

NOTE: Since I am working with quantitative variables from the Gapminder dataset, I have used the “binning” technique to re-purpose my desired variables as categorical variables.  

2. Corresponding output

(i) Column percent or “Col Pct” highlighted in green below shows the percentage of observations for each explanatory variable category (i.e. Autocracy, Anocracy, and Democracy) within the two response variable groups of the number of internet users (i.e. categorized as, high, that is >= 50, and, low, that is <50). The Col Pct shows how high or low rates of internet users differ across the three regime type categories.

Note that the categorial explanatory variable (i.e. regtype) has three levels: Autocracy, Anocracy, and Democracy. The categorical response variable (i.e. intuser) has two levels: high and low.  

(ii) Overall chi square table, where p value of <.0001 shows there is an association between number of internet users and a country’s regime type.

(iii) Data comparison between Anocracy and Autocracy

(iv) Data comparison between Anocracy and Democracy

(v) Data comparison between Autocracy and Democracy

Interpretation:

Last week, I looked at how the number of internet users varied within groups or “ranking levels” of the same regime type category (i.e. democracies, Polity scores between 6 and 10, where 6  is the lowest and 10 is the highest). This week, I chose to include the full range of regime type categories in my analysis, that is to find the variation of the number of internet users across all three regime type groupings. 

The key question remains whether the number of internet users and the regime type of countries are dependent or independent; in other words, is the number of the internet users equal across each regime type category (null hypothesis), and if they are not equal (alternate hypothesis), where do these differences appear among the distinct regime types.

In order to confidently reject the null hypothesis, I have used the Bonferroni Adjustment of the p value (p/c, where p=0.05 and c=number of comparisons) to perform comparisons for each pair of regime types across the high and low groups of internet users categories. 

I will be conducting a total of three comparisons, and the adjusted p value is 0.017 or less to reject the null hypothesis and to avoid type 1 error. 

Comparison #1 between Anocracy and Autocracy show a significant p value of 0.0004, which is less than the adjusted p value of 0.017 for a three-paired comparison. Comparison #2 between Anocracy and Democracy also show a significant p value of  <0.0001. Comparison #3 between Autocracy and Democracy has a higher than the adjusted p value, that is 0.0973. 

Notice that the p value is most significant in comparison #2 (i.e. Anocracy and Democracy), and least significant in comparison #3 (i.e. Autocracy and Democracy). 

SAS syntax used to run ANOVA and post hoc test (i.e. Duncan Multiple Range Test):

Corresponding output:

1. ANOVA

2. Box plot

3. Duncan Multiple Range test

Interpretation:

In this analysis, I am testing the association of the number of internet users (per 100 people) with the level of democracy (e.g. high vs. low). 

I have subset the data to include only countries that have Polity scores between 6 and 10, or belong to “democracy” regime type. I am using the Gapminder dataset, and have chosen to test the association between the number of internet users (per 100 people) and the level of democracy (i.e. 10 being the highest, and 6 being the lowest) of countries.  There are five levels to this explanatory variable, e.g. 6 / 7 / 8 / 9 / 10.

The null hypothesis here is that the means of the number of internet users of all levels are equal within the same grouping or in this case “democracies”, and the alternate hypothesis is that not all the means are equal.

The overall F test is significant ( F = 19.14, p = < .0001 ), indicating that there is an association between number of internet users (per 100 people) and the level of democracy.  The Duncan Multiple Range test shows where the differences lie between the five levels of democracy, i.e. 10 being the highest and 6 being the lowest levels. Where the number represents the level of democracy, countries that are not significantly different are 9 and 8; 8 and 7; and, 7 and 6. Where the number represents the level of democracy, countries that are significantly different are 10 from all the rest; 9 from 7 and 6; 8 from 10 and 6; 7 and 6 from 10 and 9.

SAS syntax for data steps and proc sort/freq steps:

SAS syntax for vertical bar charts (i.e. univariate and bivariate graph):

1. Univariate graph of internet users (per 100 people):

This graph has a skewed-right distribution. Most of the frequencies are concentrated in the lowest category (i.e. less than 25 internet users per 100 people). The frequencies decrease steadily in categories that chart countries with higher than 25 internet users per 100 people.

2. Univariate graph for female employees age 15+ (% of population):

The graph is unimodal with the highest peaks, or the most frequencies, in the 40%-59% range. This graph is also skewed to the right, as most frequencies occur in the lower categories (i.e. less than 60% of total population) than the higher categories (i.e. higher than 60% of total population). 

3. Univariate graph for oil consumption per capita (tonnes per year and person):

This graph has a skewed-right distribution. Majority of the frequencies occur in the lowest category (i.e. less than 1 tonne of oil consumption per capita), and the frequencies lessen, as well as even out, when charted for countries with more than 1 tonne of oil consumption per capita.

4. Bivariate graph for regime type (categorical explanatory variable) and internet users (quantitative response variable):

This graph has bimodal distribution with concentrations of frequencies at two intervals of the categories, that is at -8 Polity score representing autocratic countries, and 10 Polity score representing democratic countries. 

This week I have collapsed my data further and grouped these categories, including “Missing” type for missing observations, in each frequency table. The results show that out of 213 countries,

-  There are 23 institutionalized autocracies (10.8%) and 90 institutionalized democracies (42.2%). 

- For “intuser” that tracked worldwide internet access in a country’s population, the majority of countries (i.e. 81 countries) have less than 25 internet users per 100 people (38.03%). Only 11.74% of the countries (i.e. 25 countries) have 75 internet users or higher per 100 people. Most people in the world still have no access to the worldwide internet.  

- For “ocump” that tracked oil consumption per capita, 14.55% of the countries (i.e. 31 countries) consume less that 1 tonne of oil per year and person, whereas only 2.35% of the countries (i.e. 5 countries) consume 4 tonnes or higher. There are 150 missing observations; that is almost 70.42% of countries have no available data on oil consumption per capita rates. Going forward, I may rethink including this variable as there is a lot of missing data.

In week 2, I have added new variables in my analysis and I have also slightly refined my research interests at this point. I want to analyze the impact of Polity regime (i.e. autocracies and democracies) on specific social and economic indicators within society. 

In other words, I could analyze the differences (e.g. higher or lower rates) of specific indicators (e.g. social, employment, energy consumption) among institutionalized autocracies (with Polity scores from -6 to -10) and institutionalized democracies (with Polity scores from +6 to +10). 

Above, I have listed possible examples of frequency tables of these new variables to use in this analysis, such as the female employees age 15+ (% of populations) and oil consumption per capita (tonnes per year and person), as well as the number of internet users. 

Of the total sample of 213 countries in the Gapminder dataset, there are 23 institutionalized autocracies and 90 institutionalized democracies. That means approximately 10.8% of countries are institutionalized autocracies and 42.2% of countries are institutionalized democracies. 

There are 52 countries that have not been assigned any Polity scores within the dataset, and therefore will be excluded from further analysis. The countries with Polity scores between -5 to +5 (e.g. anocracies) will also be taken out of this analysis. 

Only autocracies (-6 to -10) and democracies (+6 to +10) impact on specific indicators will be analyzed. 

Data set:

The data sets that I have chosen for this study are Gapminder’s 2010 internet users (per 100 people) and 2009 democracy score (aka polity score).

 Research question:

Does internet use rate have an impact on a country’s polity score?

 Hypothesis:

High internet use is linked to high polity scores.

 Literature review:

1. Nisbet, E. C. et al. (2012). Internet use and democratic demandsL A multinational, multilevel model of internet use and citizen attitudes about democracy. Journal of Communication, 62, 249-265.  

The results from this study indicate that Internet use, but not national Internet penetration, is associated with greater citizen commitment to democratic governance.

 2. Groshek, J. (2009). The democratic effects of the internet, 1994 to 2003: A cross-national inquiry of 152 countries. International Communication Gazette, 71(3).