Negative Outlook and Submissive Behavior

I would like to explore the nature of such depressive behavior with the assumption of utility-maximization. The primary question I ask in this paper is twofold: (1) Why do people behave in a such manner when they are depressed, and (2) What are the variables that are correlated to such submissive behavior? As a person who has personally underwent depression and received clinical therapy, this topic interests me personally and find potential answers to above questions very useful.

Most convincing theory of depression comes from evolutionary psychologists, who thinks that depression is the evolutionary consequence of ancestral behavioral patterns that was evolutionarily advantageous. Price (1972) 1 suggests that depression “evolved in the context of intrasexual selection with the function of limiting fighting.” Also known as the social-rank theory, it puts forward the two following propositions: (1) Animals have been competing each other for essential resources such as territory or sexual opportunities; (2) Animal who lose needed to have an internal mechanism to manage their aggression.

Simply put, when faced with a competition, an animal can either escalate or de-escalate the situation. If she believes her chance of victory is high, she will likely decide to escalate the situation, by threatening or overpowering her opponent. If she believes otherwise, she will likely choose to de-escalate the situation, by backing off or giving up. It is critical for animals’ survival to have a sound de-escalation strategy, or else she will be harmed in the process.

Therefore, we can view a lack of engagement as a defensive mechanism in which one tries to maximize their utility by reducing their risk of failure. Adopting these ideas, we can generate an economic model that can clarify why people behave in such manner from a rational perspective.

Out of several factors provided by the survey, one factor stands out as a measure of engagement with the outside world: number of text messages sent. Text messages are a primary means of communication for young adults and college students, and a lesser number of daily messages interchanged may signify that an individual is not establishing a good social connection with the rest of the world and arguably, engaging in a submissive behavior. Therefore, I am going to use the number of daily text messages exchanged, numTxtMsg, as my dependent variable. Independent variables include those that can serve to possibly measure a student’s outlook. The primary independent variable is worried, which describes how worried a student is about his or her prospects in the job market. The variable expIncome, which measures a student’s expected future income, and patIncome, which measures a student’s parental income, can also serve as a proxy to how a students sees his or her future outlook.

I also would like to see the effect of major, tobacco, desired number of children (numChild), and school/life satisfaction (schlSat/lifeSat) to see if they have a meaningful impact to the dependent variable. Also, the number a student met his or her professor and teaching assistant, with variable names metProf and metTA respectively, might also be relevant as students who see their professors or teaching assistants less often may feel more worried about their future.

The statistical model to analyze the correlation between the dependent variable and independent variables is as follows:

I hypothesize that there is a negative correlation between numTxtMsg and independent variables worried, major, schlSat, lifeSat. The rational for the negative correlation between numTxtMsg and worried is simple, as it is the main thesis of this paper and higher value corresponds to a state of higher worriedness. With regards to the variable major, I noticed that students with lower value (1–2, Math or natural sciences & Engineering) have a higher expected income and a better employment prospects, and therefore concluded that these students should have better life prospects. As my thesis is that those with better life prospects communicate more with the outside world, I think the number of text messages must be higher for those with lower major value. For school satisfaction and life satisfaction, because higher value represent higher state of dissatisfaction, and therefore a relatively more negative outlook, I concluded that there must be a negative correlation between the dependent variable and these two independent variables.

I hypothesize that other variables, which are consisted of expIncome, patIncome, tobacco, numChild, metProf, and metTA, are positively correlated with the dependent variable of numTxtMsg. Expected income and parental income serve as a proxy for a student’s self-evaluated future prospects, and therefore a higher value should result in more communication. With regards to tobacco use, it is generally believed that higher tobacco is use is associated with mild level of depression, and as higher observed value represent a lower tobacco use, I expect a positive correlation. Number of children is interesting, as I could not find any study directly linking number of desired children to self-esteem. However, because more children require more expenditures, and as this indirectly suggest that one is expecting to have more resources in their future, I associate this variable to have a positive correlation with one’s future prospects, and therefore I expect it to be positively correlated with the dependent variable. MetProf and metTA are positively correlated with the dependent variable because I believe seeing professor or teaching assistant more often make feel student more confident about the subject matter and in result, their professional career and outlook.

I present two regression analysis of the same model presented above, one with OLS standard error and another with robust standard error:

First and foremost, there is a clear correlation between the state of worriedness and the number of text messages that students send out each day. For both OLS model and robust model, the correlation is significant at a five percent confidence level. The regression shows that for each level (out of three) of worriedness, the number of text messages decrease by about 20. Given that the average number of text messages that each student sends per day is about 70, this result is not only statistically significant but also significant in magnitude.

As for other variables, school satisfaction (schlSat) is shown to be significant for both OLS and robust model, although at varying p-value. In the OLS model, the correlation is significant at one percent confidence level, while in the robust model the correlation is significant at ten percent level. With that being said, the direction of the correlation is opposite of what I expected. I hypothesized that students who are dissatisfied will tend to send less messages, but opposite turned out to be true. Therefore, I cannot reject my null hypothesis.

Now, why would this be the case? I think that students who are dissatisfied about the school turned out to be more communicative because they must be sharing their ideas more frequently with other students. Alternatively, students who expressed dissatisfaction with the school are more confident in expressing their opinions, and more confident about themselves and their personal traits in general. This result was pleasantly surprising.

As for other variables, the variable metProf did present itself to be significantly correlated with the dependent variable, in the anticipated direction, but only in the OLS regression model. What is interesting, however, is that the variable metTA was significant in the opposite direction from what I originally hypothesized. In other words, the time in which the students spent with the professors was positively correlated with numTxtMsg, but the time in which they spend with he teaching assistants was negatively correlated with numTxtMsg. One possible explanation of this phenomenon is that, students who see their professors instead of their TA are more confident in general. Students who refrain from meeting the professor may do so because they do not want to embarrass themselves or they may think that they are wasting their professor’s time (and thus becoming an inconvenience for the professor). Both of these variables lost their significance in the robust model due to the much higher standard error.

All other variables are not shown to be significant. The variable parental income came close to being significant with a p-value of 0.12 in the robust model, but the magnitude of the correlation was relatively small. To my surprise, the variable tobacco and numChild was shown to be not significant at all, although the direction of the correlation was something that I expected to see. I think both of these variables were too weak of a predictor for number of text messages exchanged.

In this section, I will test for heteroscedasticity. I am concerned about heteroscedasticity primarily because the dependent variable numTxtMsg is a continuous variable with a wide range, and it is skewed to the left.

One of the easiest method to detect heteroscedasticity is to plot the residuals against the fitted values. While this is not an official test for heteroscedasticity, it is an easy and intuitive way to discover patterns.

The above graph clearly shows a linear relationship between yhat and the residual. Specifically, the residual decreases linearly as yhat increases. I presume that if our heteroscedasticity takes the form h(x), such that u2 = σ2h(x), h(x) = αx­, where α < 0­.

In order to officially test for heteroscedasticity, I can use Breusch-Pagan test. The Breusch-Pagan test regresses the squared OLS residuals against all independent variables. The test produces a chi-squared statistic of 389.59 with 10 degrees of freedom. This is equivalent to a significance level of 0.0000, and therefore it we can conclude that heteroscedasticity is detected. Due to this heteroscedasticity, we should use the heteroscedasticity-robust estimation model to study the true effect of our independent variables to the dependent variable numTxtMsg. Alternatively, since the form of heteroscedasticity can be derived, we can also transform the original model to produce to produce a homoscedastic model.

I will also test for outliers. The residual plot above (Graph 1) shows that there are a few outliers in the observation. Notably, the six individuals with residuals of above 200 can be classified as outliers. There is one individual with residual of above 800, who can definitely be classified as an outlier. The important question to ask is: should these individuals be considered as outliers or influential observations? If we use a scatter plot comparing numTxtMsg to worried, we can see that a majority of students, regardless of their state of worriedness, sends between 0 and 200 text messages. However, outliers are only observed from the students who fell less worried. This tells us that the negative effect of worried to numTxtMsg is driven largely by a handful of outliers. For this reason, I think the observed outliers are influential, and they should not be dropped.

There is one major variable that is clearly omitted from this study, which is self-esteem. There wasn’t a question in the questionnaire that directly addresses a student’s perceived self-esteem, and therefore I had to use several other variables, namely worried, as a proxy variable. Other included independent variables are all, to a degree, used to approximate the student’s self-esteem to address this issue of omitted variable bias. Additionally, there are variables that are left out, such as cumGPA, race, health, heightInches, and weightPounds, which can all influence a student’s perceived self-esteem. However, given the relative strength of the variable worried, and considering that the state of worriedness is often used as a proxy variable for self-esteem in psychological literature, I am relatively confident that the effect of omitted variable bias with regards to self-esteem is well addressed.

Another significant variable that was omitted, and unfortunately not accounted for, is a student’s personality. In particular, a student’s extroverted/introverted nature may significantly influence the number of text messages a student sends out each day. It is regretful that there were no variables that could be used as a proxy for this variable. If there was a way to distinguish the extroverted students from introverted ones, such as MBTI personality test results, I think I could have had a much more sophisticated finding.

There is a reason to believe that reverse causality exists in this study. Notably, student who sends a smaller number of text messages may feel more worried due to his or her lack of communication with his or her peers. Additionally, student who sends a smaller number of text messages may report lower school satisfaction and/or lower life satisfaction due to the same reason. However, I maintain my belief that the effect of worried to numTxtMsg is much greater than the other way around, because there is a tendency among students to be less communicative when they feel worried and consequently less self-confident, as indicated by several pathological studies.

In this paper, I tried to understand the relationship between depressive behaviors, mainly lack of communication, and one’s perceived self-esteem. I find a statistically significant correlation between the independent variable worried, which serve as a proxy variable for self-esteem, and dependent variable numTxtMsg, which serves as a proxy variable for communication & engagement. While most of my other dependent variables are shown to be not statistically significant, the effect of worried was notably strong, and I feel like this result reinforces the results discovered by other statisticians and psychologists.

The functional form test showed that the error of misspecification is definitely present, and the test for heteroscedasticity showed that there is an indefinable form of heteroscedasticity. In light of these findings, I would like to propose my final result in the table below, which uses a log form for my independent variable worried and robust regression. Ideally, the original model can be transformed to eliminated the effect of heteroscedasticity since the form of heteroscedasticity can be derived.

The biggest limitation of this study is twofold. First, I was not able to control for the effect of different personality to the dependent variable numTxtMsg. I think extroverted/introverted personality types would have had a significant effect onto the number of messages sent by an individual. Second, the biases introduced by measurement errors cannot be overlooked. The independent variables such as worried are subjective and self-reported measures of self-confidence, and therefore cannot be perfectly reliable.

Nevertheless, there is a degree of truth embedded to my findings, and it concerns a deep problem that is engraved into society and human nature. The issue of depression and lack of engagement is a serious and costly, and I hope a healthy balance between anxiety and personal success can be achieved through intervention and deeper understanding of the human ego.

Zheng, Yajing, Xiaohang Wu, Xiaoming Lin, and Haotian Lin. “The Prevalence of Depression and Depressive Symptoms among Eye Disease Patients: A Systematic Review and Meta-analysis.” Scientific Reports 7, no. 1 (2017). Accessed October 31, 2018. doi:10.1038/srep46453.

Sobocki, Patrik. “Cost of Depression in Europe.” The Journal of Mental Health Policy and Economics 9, no. 2 (June 9, 2006): 87–98. Accessed October 31, 2018. doi:1091–4358.

Kessler, Ronald C. “The Costs of Depression.” Psychiatric Clinics of North America 35, no. 1 (March 2012): 1–14. Accessed October 31, 2018. doi:10.1016/j.psc.2011.11.005.

Engel, G. L. & Schmale, A. H. (1972). Conservation-withdrawal: a primary regulatory process for organismic homeostasis. A Symposium of Physiology, Emotion, and Psychosomatic Illness, (pp.57±85). Elsevier : Amsterdam.

Nesse, R. M. (1990). Evolutionary explanations of emotions. Human Nature 1, 261±289.

Gilbert, Paul, and Steven Allan. “The Role of Defeat and Entrapment (arrested Flight) in Depression: An Exploration of an Evolutionary View.” Psychological Medicine 28, no. 3 (1998): 585–98. doi:10.1017/s0033291798006710.

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