Wellbeing Heterogeneity within and Among University Students

Abstract

The widespread international concern over the low average wellbeing of university students shows no sign of abating. Neglected in the debate is a recognition that wellbeing itself is multidimensional and not all components respond in the same way to external and internal pressures. We draw on a large sample survey of first year students who enrolled in a New Zealand university in 2019 and measure their wellbeing using the WHO-5 measuring instrument. Instead of modelling the index itself we address its five individual components. We apply the marginal (population-averages) model using the generalised estimating equation (GEE) method. As well as confirming earlier findings that students with poorer physical health and lower financial capacity experience lower levels of wellbeing, we document their uneven influence on the relative frequency with which the five individual components are experienced: being cheerful, calm, active, fresh and interested over the previous two teaching weeks.

Introduction

There is an ongoing international and domestic concern over the wellbeing of university students. Levels of anxiety, depression and suicide ideation have been rising with each successive cohort in what some now describe as an epidemic.¹ The widespread reduction in wellbeing poses a challenge to university administrations many of whom lack evidence beyond reports from their student counselling services. Student counsellors only see a small, unrepresentative, minority of students even today because help seeking remains stigmatised among young adults.² An understanding of the complete distribution of wellbeing on campus requires at least the administration of screening instruments to a representative sample of all enrolled students.

Screening instruments are typically constructed by summing Likert Scale responses to the set of questions asked. The resulting index is then regressed, usually as continuous variable, against a set of predictors to estimate the influence of gender, age, health, personality, resilience, and a range of other attributes of interest. While valuable, these studies rarely go on to investigate how the individual components of their wellbeing index behave – that is how the different sub-scales respond to the arguments of interest. For example, as we report below, wellbeing is not only lower among students with poorer physical health and greater financial pressures but the component moods of cheerfulness, calmness, activity, freshness, and interest in daily life used to compile the index also vary in response.

Our study begins with a brief review of the international attention being paid to the mental health of university students. We then introduce the YOU Student Wellbeing Survey which we administered to the 2019 cohort of first year students in one of New Zealand’s main universities.³ This is followed by a description of our primary measuring instrument, the WHO-5 wellbeing index, its empirical distribution and its individual components.

We estimate a binary logit model on each component of the wellbeing index (each collapsed into high frequency occurrence = 1 vs low frequency = 0) from which we post-estimate the probability students experience each mood over more than half the previous fortnight given their level of physical health, ability to meet financial commitments, age, and sex. We then apply the ordinal model to estimate effects of the arguments on the full range of frequencies over which each mood is experienced. Our graphical depiction of the results provides the university administration with a detailed profile of the wellbeing influence of the two major drivers of student wellbeing on older and younger male and female first year students.

University Student Wellbeing

In one of the first published papers to draw attention to the mental health of tertiary students, Sarah Stewart-Brown and colleagues at the University of Oxford undertook a survey of three UK higher education establishments in 1995. They concluded that, “the health of students is poor relative to that of their peers, and that their emotional health is more a problem than their physical health.”⁴ “Public health practitioners”, they urged, “might want to pay more attention to the health of this important and relatively neglected group. Worries about studies and money appear to be affecting students’ academic work, and this should be of concern to higher education establishments” (Stewart-Brown et al., 2000: 492).

The same message was issued by the Royal College of Psychiatrists a decade later (Royal College of Psychiatrists, 2011). Of particular concern was the trajectory—the fact that the proportion of affected tertiary students was growing. The number of young students in higher education with mental disorders was increasing (Castillo & Schwartz, 2013; Eisenberg et al., 2007) as was the severity of the psychological problems presented at counselling services (Hunt & Eisenberg, 2010; Kadison & DiGeronimo, 2004; Sarmento, 2015; Zivin et al., 2009). The literature on university student wellbeing has now expanded correspondingly (Holm-Hadulla & Koutsoukou-Argyraki, 2015). Reviews include Robotham and Julian (2006), Storrie et al. (2010), Sales et al. (2001), Stewart-Brown et al. (2000) and Auerbach et al. (2018). The pressure on the mental health of university students has been well documented in Australia (Stallman, 2010; Cvetkovski et al., 2012, 2017, 2018; Farrer et al., 2016; Leahy et al., 2010, Larcombe, 2016), in the USA (Byrd & McKinney, 2012; Castillo & Schwartz, 2013; Eisenberg et al., 2007; Zivin et al., 2009) and Canada (Adlaf et al., 2001). Several studies have been carried out in the United Kingdom (Bewick et al., 2010; Cooke et al., 2006; Denovan & Macaskill, 2017; Macaskill, 2013; Macaskill & Denovan, 2014,) as well as the Republic of Ireland (Houghton et al., 2011), and now New Zealand (Morrison et al., 2023).⁵

European studies have been conducted in Germany (Mikolajczyk et al., 2008), Norway (Nerdrum et al., 2006), the Netherlands (Boot et al., 2009) and Hungary (Biro et al., 2010). Similar findings are now emerging from developing countries (January et al., 2018) such as Nigeria (Adewuya et al., 2006). Consistent results are reflected in the differential effect of COVID-19 in Chinese universities Cao et al (2020), Li et al (2020) and Li et al (2021) and Hong Kong (Wong et al., 2006).

Among the strongest influences on wellbeing are the students’ physical and financial health. Physical health is strongly affected by mental health status (Momen et al, 2020; Suldo et al., 2016; Ansari et al., 2011; Veenhoven, 2008; Roberts et al. (2000), and that the reverse is also true (see Renshaw & Cohen, 2014, esp. Table 5 p 327–8 Scott et al., 2016). The presence of a two-way effect is well recognised because, in addition to being internally related, mental, and physical health are both subject to common contextual influences (Roberts et al, 1999).

Our second variable of interest is the students’ assessment of their financial capability. While the university student wellbeing literature has paid relatively less attention to this effect (Andrews & Wilding, 2004 and Denovan & Macaskill, 2017), Richardson’s study of British undergraduate students has shown how, “Greater financial difficulties predicted greater depression and stress cross-sectionally, and also predicted poorer anxiety, global mental health and alcohol dependence over time.” (Richardson, 2016: 344). Joo et al. had also observed how, “The cycle of needing money, working, and academic performance could “spiral into academic interruption” (Joo et al, 2008:302). In a contemporary UK study McCloud found that, less income, more loan income, more total expected debt and experiencing more financial difficulties were all associated with more symptoms of depression in students (McCloud, 2022). Not surprisingly there have been calls for further research on how lack of social, financial and material resources can lead to the emergence of poor mental health in students.

Notwithstanding the attention received in the university student wellbeing literature few researchers have attempted to measure the association of the students physical and financial health with the individual components of the wellbeing indices they use. The distinctions between the five components of the WHO-5 index we use below—cheerfulness, calmness, activity, freshness, and interest in daily events—are important not only in identifying how differences in physical and financial health manifest but also because of their potential to inform alternative interventions.

In summary, the wellbeing of university students is far from being an isolated phenomenon confined to a few institutions in specific countries. It is now a global phenomenon which has attracted substantial academic attention as well as a growing list of practical responses (Baik et al., 2017, 2019; Larcombe et al., 2022). At the same time student wellbeing is extremely varied and heterogeneous in nature and is subject to many influences including the students’ physical health and financial constraints. Approaches which expose this variation, in addition to age and sex, can be very helpful to university administrators responsible for monitoring student mental health.

Data

The administration at Victoria University ran four Student Experience Improvement Surveys (SEIS) between 2014 and 2017, adopting a model previously trialled in Australia (Radloff, 2011; Radloff et al., 2011).⁶ The primary purpose of the SEIS was to inform respective administrations of the extent to which students were using and were satisfied with the range of student services the university was offering.⁷ However, in a departure from most other New Zealand university student surveys, the SEIS also included a screening instrument for student wellbeing, the WHO-5.

The lower than expected average wellbeing of students discovered in the SEIS results, together with rising counselling numbers and anecdotal evidence from across campus, helped focus attention on the issue of mental health. By 2018 both staff and students had recognised the need for an independent survey which focussed specifically on student mental health rather than just their utilisation of university services. The result was the YOU Student Wellbeing Survey, the label ‘YOU’ being suggested by the students themselves.⁸

Following an advertising campaign run by the university’s communication team the full survey of 139 questions under 28 topics was sent electronically via Qualtrics to over 4000 first year students in April/May 2019, two months after start of the first term.Students were given two weeks to complete the survey and they did so in an average elapsed time of about 20 min. A total of 1591 students returned their answers, an overall response rate of over 35 percent.⁹ All but 8 students consented to the research team using their anonymised answers.¹⁰

In summary, the YOU Student Wellbeing Survey administered independently by academic and professional staff at Victoria University was designed to address a growing concern over the mental health of university students. A sample of over one and a half thousand first year students answered nearly 140 questions covering a wide variety of topics including several measures of wellbeing itself.

Measurement

There is no consensus as to how mental health should be measured (Barkham et al., 2019) and a wide range of different instruments have been applied (Linton et al., 2016). Most studies only employ one measure although several focus on differences between them, e.g. Koteles and Simor (2014). This paper focuses on responses to the first of our measuring instruments, the World Health Organisation’s WHO-5 index.¹¹

In addition to being used as a depression screener in medical settings (Topp et al., 2015), the WHO-5 index has been used in several studies of tertiary student wellbeing; see for example Downs et al. (2017), Alessandri et al. (2020), Koteles and Simor (2014) and Preoteasa et al. (2016).¹² The instrument has also been subject to several methodological interrogations (Bech et al., 1996, deWit, 2007; Sischka et al., 2020; Krieger et al., 2014).

Most single index studies of mental health focus on the mean of their selected index as well as its standard deviation and skewness (Huppert, 2009). The mean score of 53.8 from the YOU sample is only slightly higher than internal benchmark for depression of <  = 52 on the percentage scale (Downs et al, 2017).¹³ The distribution shown in Fig. 1 has a standard deviation of 17.06 either side of the sample mean of 53.8 percent (dashed lines) with three quarters of the surveyed students returning WHO-5 percentage scores between 24 and 68. While some students are clearly flourishing, others within the longer left hand tail are languishing by comparison. The overlaid normal distribution highlight’s the slight negative skew of the sample distribution.

Fig. 1

Distribution of WHO-5 index scores over first year university students, 2019. N = 1540

The variables of interest in our study are the two YOU survey variables with the strongest impact on wellbeing—the students self-assessed physical health and the students perceived ability to meet their financial commitments. The physical health question asked “How is your physical health in general? Would you say it is: Very bad, Bad, Fair, Good, Very Good? The financial capacity question, in turn, reads: “Over the past 6 months, I have had difficulty in meeting my financial commitments.” The response options were: Strongly disagree, Disagree, Neutral, Agree and Strongly Agree.

The positive link between the students’ wellbeing and their physical and financial health is apparent from the margins plots in Fig. 2 from two separate regressions of the WHO-index on the two factor variables. The average percentage wellbeing score ranged from the 40.28 percent in the case of those students in ‘Very Bad’ physical health up to 64.05 percent in the case those in ‘Very Good’ health, a difference of 23.77 percent. Over 15 percent of the variance in wellbeing was accounted for by these differences in physical health.

Fig. 2

The relationship between the WHO-5 index and student assessment of their physical and financial health, 2019 (Sample sizes are 1527 and 1507 respectively as a result of missing values)

The experienced range and magnitude of effect on wellbeing was less marked when it came to the students’ financial health. The average wellbeing of those who strongly agreed they had difficulty in meeting their financial commitments was 42.56 percent compared to 57.69 percent for those who strongly disagreed, a difference of 15.13 percent. Only 4.5 percent of the variance in wellbeing could be attributed to differences in financial health. The variations in physical and financial health together accounted for almost 18 percent of the variance in the wellbeing index. The interaction between the two arguments was weak and statistically insignificant.

The positive link between the mental and physical health of university students we found through the YOU survey replicates the positive relationship found in other studies (Diener et al., 1998; Ohrnberger et al., 2017; Roberts et al., 2000).¹⁴ The same is true of the negative influence of financial constraints which has been documented by Roberts et al (1999), Jessop et al., (2005) and Joo et al., (2008) and more recently by McCloud (2022).¹⁵

While many studies have expanded our knowledge of university student wellbeing and its correlates, we remain unaware of any published studies which go beyond assessing their impact on the wellbeing indices they use. This is a little surprising because as we show below the relative weights of the five components used to construct the WHO-5 index vary in response to differences in the students’ physical and financial health. Confining analysis to the wellbeing index alone prevents researchers from learning about how the different components of wellbeing behave. We turn therefore to modelling the variation that takes place within the index.

Inside the WHO-5 Index

The WHO-5 index is constructed from five simple and non-invasive questions which tap the subjective wellbeing of respondents over the two weeks to which it is applied.¹⁶ In our case the first year students were asked to record how often over the two teaching weeks prior to the survey they experienced each of the five different moods.¹⁷ The response to each question was scored on a six category Likert scale, coded from 0 (at no time) to 5 (all of the time). As Table 1 explains, students were asked whether they had felt cheerful and in good spirits, calm and relaxed, active and vigorous, whether they woke up feeling fresh and rested and whether their daily life has been filled with things that interest them. We refer to this variable simply as Question in the results below.

Table 1 The WHO-5 wellbeing index

The individual components of the WHO-5 do not replicate the distribution of the index in Fig. 1. Each component contributed differently to the total as shown in Fig. 3. Their mean scores varied from 3.15 in the case of the cheerful component and 3.11 in the case of interest, to 2.7 in the case of calm, 2.5 in the case of active, down to 2.02 when it came to feeling fresh and rested. While component 1, 2 and 5 are negatively skewed like the overall index, this was not the case for active (3) which shows little skew, and feeling fresh and rested (4) which was positively skewed.

Fig. 3

Responses to the five WHO-5 questions. N = 1542

In summary, we have measured student wellbeing using a well validated measuring instrument, the WHO-5, which has been applied to many populations including several university student samples. Of particular interest is the fact that the wellbeing distributions is very wide, ranging from students whose high mental health suggest they are flourishing down to those whose wellbeing scores are low and appear to be languishing. While most previous studies of university students’ wellbeing have addressed the variation in the index across the student body, our concern is with the way variation within the index varies across students given their varying levels of physical and financial health.

Method

In order to motivate our substantive concern and choice of method we offer the following two scenarios.

Under scenario 1 imagine you are a doctor in a university student health clinic and you want to know how much a given improvement in the individual student’s physical health would raise the odds of them experiencing each of the five component moods that make up the WHO-5 index more than half the time over the prior fortnight.

Under scenario 2 imagine you are working for the Vice-Chancellor who is taking seriously the university’s collective wish to raise student wellbeing. The VC wants to know how different levels of students’ physical and financial health are associated with the frequency with which they experience the different moods.

Under the first scenario the service professional wants to know the subject- specific odds that a student with known health characteristics will experience the wellbeing moods more than half the time. Under the second scenario the head of the university wants a prediction for the margin or population average, over the entire cohort of first year students. For example the university administration might want to know how frequently students rate their health as poor, or felt calm and relaxed over the preceding two weeks. Given the potential financial implications the VC might also wish to know how likely students who had difficulty in meeting their financial commitments continue to feel active and vigorous.

Applying a subject-specific linear regression model would serve the doctor’s needs as the estimates would tell her how the frequency a given mood was experienced by students reporting a given level of physical health or ability to meet their financial commitments. In contrast, applying the population-average or marginal model would tell the VC how the average probability of experiencing a given mood more than half the time over the same two weeks would differ between groups of students. For example, to what degree would younger students with given levels of physical and/or financial health differ from older students when it came to the odds of their being cheerful, calm, active, fresh and interested? In other words, our choice of the subject-specific or marginal model would depend on whose question we are trying to answer, the doctor in scenario 1 or the Vice-Chancellors in scenario 2.¹⁸

When multiple responses are answered by the same individual either at one point in time or over time the responses share a commonality and end up being more highly correlated than the same questions answered by different individuals. In the case of our YOU survey within person correlations occur when the same student answers the five individual questions used to generate the WHO-5 index. One method for addressing such clustering is the general linear mixed model. Another is the marginal model fitted using the generalised estimation equations (GEE) (Heagerty & Zeger, 2000). We introduce the marginal model and then outline the GEE method.

The Marginal Model

Suppose there are ${m}_{i}$ correlated responses for each subject (sampled students in our case). For the ${i}^{th}$ subject, $i\in \{1,...,n\}$, ${Y}_{i}=\left({Y}_{i,1},...,{Y}_{i,{m}_{i}}\right)\mathrm{^{\prime}}$ denotes the ${m}_{i}$-dimensional response vector. The vector ${X}_{i}$ denotes the $p$-dimensional corresponding predictor vector. Let the marginal mean response be $E\left({Y}_{i}|{X}_{i}\right)={u}_{i}$. We have $\left({u}_{i}\right)={X}_{i}\mathrm{^{\prime}}\beta$, where $g$ is the link function of choice and $\beta =\left({\beta }_{1},..,{\beta }_{p}\right)\mathrm{^{\prime}}$ is the vector of regression parameters. Assuming ${V}_{i}$ is the ${m}_{i}\times {m}_{i}$ working variance–covariance matrix for ${Y}_{i}$, the estimates of $\beta$ are obtained by solving the following estimating equations:

$$\begin{array}{c}U\left(\beta \right)=\sum_{i=1}^{n}\frac{\partial {u}_{i}}{\partial \beta }{V}_{i}^{-1}\left({Y}_{i}-{u}_{i}\right)=0\end{array}$$

For our study we propose a binary logistic model and an ordinal logistic model with proportional odds for the two data types respectively. To select the best set of predictors, we use a backward elimination strategy. Backward elimination starts with all candidate predictors (five main effects, $Question$, $Age$, $Gender$, $Finances$, $Health$ and all of their two-way interactions), then tests and deletes the least significant interaction one at a time until all remaining interactions are significant at $\alpha =0.05$. A main effect is tested only when no interaction associated with it is left in the model.

A binary logistic model is suitable for the type of data described in Table 1 if the wellbeing responses have only two classification levels, a low frequency one in which 0 = wellbeing $\in \{0,1,2\}$ and a high frequency one in which 1 = wellbeing $\in \{3,4,5\}$. Frequency refers to the number of times the mood is experienced by the student over the two teaching weeks preceding the survey. The optimal model from backward elimination has five main effects: $Question$, $Age$, $Gender$, $Finances$, $Health$; and four interactions: $Question$&$Age$, $Question$&$Gender$, $Question$&$Finances$, $Question$&$Health$.

The model can be further described as follows.

$$\mathrm{logit}\left(\Pr\left(Y_{i,t}=1\right)\right)=\log\left(\frac{\Pr\left(Y_{i,t}=1\right)}{1-\Pr\left(Y_{i,t}=1\right)}\right)$$

$$=\beta_0+\beta_t^Q+\beta_{a_i}^A+\beta_{g_i}^G+\beta_{f_i}^F+\beta_{h_i}^H+\beta_{t,a_i}^{QA}+\beta_{t,g_i}^{QG}+\beta_{t,f_i}^{QF}+\beta_{t,h_i}^{QH}$$

where ${Y}_{i,t}\in \{0,1\}$,

i  is the subject (respondent),

t  is the question indicator, $t\in \left\{Cheerful,Calm,Active,Rested,Interested\right\}$,

a_i  is age, ${a}_{i}\in \left\{Under\hspace{0.33em}20,\hspace{0.33em}20\hspace{0.33em}or\hspace{0.33em}above\right\},$

g_i  is gender, ${g}_{i}\in \{Male,Female\}$,

f_i  is the self assessed financial capacity of subject $i$, ${f}_{i}\in \{Bad,Poor,Fair,Good,Excellent\}$, and.

h_i  is their self assessed physical health, ${h}_{i}\in \{Poor,Fair,Good,Excellent\}$.

The constraints are ${\beta }_{Cheerful}^{Q}=0$, ${\beta }_{Under\hspace{0.33em}20}^{A}=0$, ${\beta }_{Male}^{G}=0$, ${\beta }_{Bad}^{F}=0$, ${\beta }_{Poor}^{H}=0$, ${\beta }_{t,{a}_{i}}^{QA}=0$ if $t=Cheerful$ or ${a}_{i}=Under\hspace{0.33em}20$, ${\beta }_{t,{g}_{i}}^{QG}=0$ if $t=Cheerful$ or ${g}_{i}=Male$, ${\beta }_{t,{h}_{i}}^{QF}=0$ if $t=Cheerful$ or ${f}_{i}=Bad$, ${\beta }_{t,{h}_{i}}^{QH}=0$ if $t=Cheerful$ or ${h}_{i}=Poor$. All predictor variables are categorical.

The GEE Method

Our dependent variable takes two possible forms, binary or ordinal. For example in the binary case, a student is treated as being calm if question 1 in Table 1 is experienced more than half the time ( 0,1 or 2), and 0 if less than half the time (3,4 or 5). In the ordinal case all five frequencies are modelled. A generalised linear model (GLM) links each marginal mean from the response to a linear predictor, providing a guess for the correlation structure among the responses. However, unlike a GLM which assumes independence of the observations, the GEE method assumes a within-subject correlation and independence of the subjects. The GEE method does not consider the full likelihood of data; it is quasi-likelihood based and obtains the effect of a predictor variable on the average of the population—the population average effect. Even if the speculated correlation structure is suboptimal, as long as marginal means are correctly specified the asymptotic normality of its estimators ensures that GEE inferences are robust and unbiased.¹⁹

The advantage of GEE over ordinary logistic regression is that more efficient estimates are obtained if the working correlation structure resembles the true dependence structure. A nice feature of the GEE method is that marginal effects can be consistently estimated, even if the dependence among units in clusters is not properly modelled. The standard errors are usually based on the sandwich estimator, which takes the dependence into account.

Since GEE is quasi-likelihood based, we use Wald tests to determine the overall significance of a predictor. Let ${H}_{0}:$ all ${\beta }_{k}=0$ versus ${H}_{a}:$ at least one ${\beta }_{k}\ne 0$, where ${\beta }_{k}$ is a column vector of parameters of interest. A Wald test statistic for testing ${H}_{0}$ is defined as

$$\begin{array}{c}W={\left(\widehat{{\beta }_{k}}\right)}^{T}{\left[\widehat{\text{Cov}}\left(\widehat{{\beta }_{k}}\right)\right]}^{-1}\widehat{{\beta }_{k}},\end{array}$$

where ${\text{Cov}}\left(\widehat{{\beta }_{k}}\right)$ denotes the variance–covariance matrix for $\widehat{{\beta }_{k}}$. Under H_o this statistic $W$ follows an asymptotic chi-squared distribution with degree of freedom $v$, which is the number of non-redundant parameters in ${\beta }_{k}$.

Regression parameters describe a linear relationship between the predictors and the response’s logit transformation. To aid interpretation, we convert the logit into a probability.²⁰ Suppose $X$ is the set of predictors and $\beta$ is the corresponding parameters then the logit of the probability $\mathrm{Pr}\left(Y=1\right)$ is given by

Fig. 4

The percent of first year undergraduate students who reported being cheerful, calm, active, rested and interested more than half the previous fortnight grouped according to their physical and financial health, age and sex. The binary logistic GEE model

Fig. 5

Probability of students being Cheerful, Calm, Active, Rested and Interested more than half the time in the two teaching weeks prior to the survey. Ordinal logistic GEE model

$$\begin{array}{c}{\text{logit}}\left({\text{Pr}}\left(Y=1\right)\right)={\text{log}}\left(\frac{{\text{Pr}}\left(Y=1\right)}{1-{\text{Pr}}\left(Y=1\right)}\right)={X}^{T}\beta .\end{array}$$

Letting $x$ be a vector of predictor values, solving for the probability ${\text{Pr}}\left({Y}_{x}=1\right)$, gives us

$$\begin{array}{c}{\text{Pr}}\left({Y}_{x}=1\right)=\frac{{\text{exp}}\left({x}^{T}\beta \right)}{1+{\text{exp}}\left({x}^{T}\beta \right)}.\end{array}$$

To find the confidence interval of $\widehat{\text{Pr}}\left({Y}_{x}=1\right)$, we require the variance of its logit,

$$\begin{array}{c}{\text{Var}}\left({x}^{T}\widehat{\beta }\right)={x}^{T}{\text{Cov}}\left(\widehat{\beta }\right)x,\end{array}$$

where ${\text{Cov}}\left(\widehat{\beta }\right)$ is the variance–covariance matrix of $\widehat{\beta }$. Then, the confidence interval of the logit is given by

$$\begin{array}{c}{x}^{T}\widehat{\beta }\pm Z\sqrt{{\text{Var}}\left({x}^{T}\widehat{\beta }\right)},\end{array}$$

where $Z$ is the z-score for a selected confidence level. Finally, the confidence interval of ${\text{Pr}}\left({Y}_{x}=1\right)$ is

$$\begin{array}{c}\left(\frac{{\text{exp}}\left({x}^{T}\widehat{\beta }-Z\sqrt{{\text{Var}}\left({x}^{T}\widehat{\beta }\right)}\right)}{1+{\text{exp}}\left({x}^{T}\widehat{\beta }-Z\sqrt{{\text{Var}}\left({x}^{T}\widehat{\beta }\right)}\right)}\hspace{0.33em},\hspace{0.33em}\frac{{\text{exp}}\left({x}^{T}\widehat{\beta }+Z\sqrt{{\text{Var}}\left({x}^{T}\widehat{\beta }\right)}\right)}{1+{\text{exp}}\left({x}^{T}\widehat{\beta }+Z\sqrt{{\text{Var}}\left({x}^{T}\widehat{\beta }\right)}\right)}\hspace{0.33em}\right).\end{array}$$

The confidence interval of the logit is also useful in testing whether a change in the predictor level produces a significant difference in the probability of success. One can also replace $x$ by ${x}_{1}-{x}_{2}$ to find the confidence interval of the difference in their logits where ${x}_{1}$ and ${x}_{2}$ are two different vectors of predictor values. If this interval does not include 0, we conclude that the two logits are significantly different and so are their corresponding probabilities.

Results of the Binary Model

The estimated effect on the log-odds of the selected model are reported in Table 2 (Appendix 1). The predicted probabilities (in percentage form) are presented graphically in Fig. 4. The 20 panels therein depict the reported experience of four types of student: younger and older males and females in each of four health categories and five financial capacity categories (4 × 5 = 20). The lines within each panel connect the five moods used to construct the WHO-5 index; the solid black lines connect the responses of older males (> 20 years) and the dashed black lines the younger males (< = 20 years). The solid grey lines in each panel connect the responses of older females and the dashed grey lines the younger females.²¹ The single percentage figure reported in each panel indicates their share of the sample. For example students in Good Health and Good Finances constitute 18.3 of the sample while those in Poor Health and Bad Finances only make up 1 percent.

The top left panel of Fig. 4 depicts the percentage of students who were in excellent health and excellent financial condition who reported being cheerful, calm, active, rested and interested more than half the time over the fortnight prior to the survey. They made up 3.4 percent of the sample. When students were in good physical shape and could meet their financial obligations these probabilities were relatively high, although the percentages for both younger and older females were slightly lower than their male counterparts, especially when it came to feeling calm and rested.

In marked contrast, students who were in poor health and also unable to meet their financial commitments (the 1% in the bottom right panel) were much less likely to report being cheerful, calm, active or rested. Even amongst this group however the university students’ level of interest was much less affected by their lower physical and financial health.

By comparing across the rows of Fig. 4 we can see how differences in physical health affected each component of the WHO-5 index at each level of financial capacity. Even if a student is able to meet their financial commitments the chances of their being cheerful, calm etc. is lower among those in poorer physical health. The reductions in wellbeing are not uniform however, and were more severe when it comes to reporting feeling active and rested.

Looking down the rows of each column of Fig. 4, we learn that even students in excellent physical health will experience a reduction in wellbeing if they are unable to meet their financial commitments. However the effect on each component of wellbeing is not the same. While their activity level remains high (as does their level of interest) they are considerably less calm, especially in the case of females, and less rested the less rested they are the less able they are to meet their financial commitments.

A third feature of the 20 panels in Fig. 4 is the relative constancy of the difference between the gender and age groups. Regardless of their physical health and financial status, first year female students are less likely to report being in a positive mood over more than half the previous fortnight, with the exception (again) of ‘things of interest’. This gender separation is most marked when it comes to feeling calm and rested, and in all the panels it is the older (> 20 years) first year students who are less likely to be cheerful and calm but more likely to report being active and rested.

In summary, the student’s physical health and their ability to meet their financial commitments both impact the frequency with which they report positive moods but the degree of influence differs according to their age and sex. Over half of the first year students in our 2019 sample had their fees paid by the state, and this may help explain why financial capacity had a less marked effect on their wellbeing relative to experiencing poor physical health. Being more cheerful and calm were characteristics of those who had control over their finances whereas their physical health had the greatest effect on the frequency with which they felt active and rested. Regardless of age and sex, when it came to the frequency with which they experienced ‘a daily life filled with things of interest’ health and finance had considerably less influence. Finally, when it came to the frequency with which students experienced each of the five components of wellbeing over their past fortnight we found in favour of younger male students.

We now fine-tune our analysis by expanding the intensity of the wellbeing moods to cover the full set of six frequencies over the prior fortnight each mood is experienced, from ‘at no time’ to ‘all the time’. This additional detail allows us to discern more subtle shifts in the five different moods at different levels of physical and financial health (by age and sex).

Ordinal Responses

An ordinal logistic model with proportional odds, also called a cumulative logit model, is suitable for modelling the additional durations of the different moods. A cumulative logit is defined by

$$\begin{array}{c}\mathrm{logit}\left(\mathrm{Pr}\left({Y}_{i,t}\le k\right)\right)\end{array}$$

where $k\in \{1,2,...,K-1\}$ and $K$ is the number of observed levels of the response; $k$, sometimes called a cut-off point which dichotomises the ordinal outcomes into two complementary sets. To utilise the full potential of available data, we could fit $K-1$ binary logistic models with different cut-off points and obtain a $\left(K-1\right)\times p$ matrix of all $\beta$.

This method raises the question as to how many parameters are too many? While a large number of parameters enhances model fitting it also makes the inferences less generalizable. Proportional odds assume that each predictor exerts the same effect on all cumulative logits regardless of the choice of $k$. An ordinal logistic model with proportional odds has $K-1$ intercepts, and only one set of parameters. With this compact model, one can utilise all available data and still make a concise analysis.²²

The five component moods which make up the wellbeing index now have six durations over which they are experienced in the fortnight preceding the survey, (0,1,2,3,4,5). As a result of these six classification levels the optimal model from backward elimination has five main effects: $Question$, $Age$, $Gender$, $Finances$, $Health$ and three interactions: $Question$&$Age$, $Question$&$Gender$, $Question$&$Health$. The model can be further described as follows, where signs are used to make estimators intuitive—a positive value indicates a positive effect.

$$\begin{array}{c}\mathrm{logit}\left(\mathrm{Pr}\left({Y}_{i,t}\le k\right)\right)=log\left(\frac{\mathrm{Pr}\left({Y}_{i,t}\right)\le k}{\mathrm{Pr}\left({Y}_{i,t}\right)>k}\right)\\ ={\beta }_{0,k}-{\beta }_{t}^{Q}-{\beta }_{{a}_{i}}^{A}-{\beta }_{{g}_{i}}^{G}-{\beta }_{{f}_{i}}^{F}-{\beta }_{{h}_{i}}^{H}-{\beta }_{t,{a}_{i}}^{QA}-{\beta }_{t,{g}_{i}}^{QG}-{\beta }_{t,{h}_{i}}^{QH}\end{array}$$

where ${Y}_{i,t}\in \{\mathrm{0,1},\mathrm{2,3},\mathrm{4,5}\}$; $k\in \{\mathrm{0,1},\mathrm{2,3},4\}$;

${\beta }_{0,k}$ is the intercept for cutoff $k$,

${\beta }_{0,k}\in \{{\beta }_{\mathrm{0,0}},{\beta }_{\mathrm{0,1}},{\beta }_{\mathrm{0,2}},{\beta }_{\mathrm{0,3}},{\beta }_{\mathrm{0,4}}\}$, and.

$i$ is the subject (the respondent),

$t$ is the question indicator, $t\in \{Cheerful,Calm,Active,Rested,Interested\}$,

${a}_{i}$ is age, ${a}_{i}\in$ $\{Under\hspace{0.33em}20,\hspace{0.33em}20\hspace{0.33em}or$ $above\}$,

${g}_{i}$ is gender, ${g}_{i}\in \{Male,Female\}$,

${f}_{i}$ is the finances of subject $i$, ${f}_{i}\in \{Bad,Poor,Fair,$ $Good,$ $Excellent\}$, and.

${h}_{i}$ is physical health, ${h}_{i}\in \{Poor,Fair,Good,Excellent\}$.

The constraints are ${\beta }_{Cheerful}^{Q}=0$, ${\beta }_{Under\hspace{0.33em}20}^{A}=0$, ${\beta }_{Male}^{G}=0$, ${\beta }_{Bad}^{F}=0$, ${\beta }_{Poor}^{H}=0$, ${\beta }_{t,{a}_{i}}^{QA}=0$ if $t=Cheerful$ or ${a}_{i}=Under\hspace{0.33em}20$, ${\beta }_{t,{g}_{i}}^{QG}=0$ if $t=Cheerful$ or ${g}_{i}=Male$, ${\beta }_{t,{h}_{i}}^{QH}=0$ if $t=Cheerful$ or ${h}_{i}=Poor$. All predictor variables are categorical.²³

The ordinal logistic model with proportional odds is a more generalised representation of the data compared to the binary logistic model because it considers both the ordinal nature of responses (the multiple frequency with which positive moods are experienced over the preceding fortnight) and the effect of different cut- points.

To be comparable with Fig. 4, Fig. 5 calculates the estimated probability of Y_i,t >  = 3, that is, the probability of experiencing the mood more than half the time in the previous fortnight of teaching. The panels in Fig. 5 show that the probabilities of being calm, active and rested more frequently in the last two weeks are significantly different for male and female students. The biggest difference is apparent in the case of calm, followed by active and rested. The average probability of a young male student saying they felt calm most of the time was percent higher than a young female student, but only slightly lower than older male students at $17.7$ percent. The equivalent difference when it came to the frequency of feeling active was 10.1 percent and rested, 5.3 percent. As we noted in the binary model, age makes a difference when it comes to being cheerful most of the time. Younger students have a much higher probability of being cheerful more than half the time but there is no significant difference apparent in the other four moods.

As in the binary model reported in Fig. 4 both the ability of students to manage their finances and particularly to maintain good physical health had a positive impact on their wellbeing but we found no significant interaction between financial health and age, finances and gender, health and age or health and gender.

Discussion

The low average wellbeing of tertiary students continues to receive attention across the globe. However, wellbeing itself has several dimensions and many different influences. In order to better understand both the dimensionality and the impact of key pressures we surveyed first year students enrolling in a New Zealand university in 2019. We administered the WHO-5 instrument which asks the frequency with which students have been cheerful, calm, active, fresh and interested over the previous two teaching weeks. Unlike the index itself, which is usually modelled as a continuous measure, answers to each of its component five moods are discrete responses and we therefore modelled their variation across the students by applying the logit model (binary and ordinal).

We found that the means of the five components or moods which make up the wellbeing index varied considerably, as did their variance and skewness; therefore we should not simply infer that the component scores behave in the same way as the total score, the WHO-5 index. Nor could we assume that the different components of the index varied in the same way according to the level of the students’ physical and financial health. Therefore our modelling focussed on estimating just how each of the students level of cheerfulness through their level of interest varied under different levels of physical and financial health given their age and gender.

The fact that answers to the five questions within the WHO-5 instrument were clustered within each individual student required an estimation method which was not sensitive to that correlation. In order to counter the clustering effect we employed the GEE method and estimated the marginal or population-averages model. Our application of the binary model yielded estimates of the odds of high or low wellbeing given the student’s membership of one of the 20 possible groups (5 × 4 categories) which we converted to probabilities and displayed as percentages in Fig. 4. This was followed by estimates of the ordinal model covering the six durations over which the moods were experienced, ranging from none of the time through all of the time. Their post-estimated probabilities were displayed as percentages in Fig. 5.

Our results showed that the capacity of students to make choices which raise wellbeing are particularly constrained at the lower end of the wellbeing distributions, among those with the worst health and the lowest financial capacity. In a step that sets our study apart, we have shown that the same is true of the five moods used to construct the wellbeing index—but to different degrees. The components of the overall wellbeing measure most affected by differences in physical health are feeling active and vigorous and being cheerful and in good spirits. For example, those reporting the lowest category of physical health are a quarter less likely to say their feel active or cheerful (more than half the time). While the associations are less marked in the case of being calm and rested they are still statistically significant at a difference of about 14% and 10%.

When it comes to the demographics, our results showed that male first year students were a fifth more likely to record being calm, and nearly a tenth more likely to be active and five percent more likely to being rested than were female first year students. On the other hand male students were no more likely to record being cheerful or interested in everyday life. Being younger also mattered; students 20 years of age and under were over 7 percent more likely to record being cheerful and rested more than half the time.

Limitations

Alongside the contributions we make in this paper are several limitations. Firstly, the relationships we describe are only correlational. Suggestive though they may be, their cross-sectional nature does not allow us to infer causation. Fortunately, the YOU Student Wellbeing Survey was repeated on two successive intakes, in 2020 and 2021, and a later analysis of these cohorts will allow us to test of the stability of the above estimates. In addition, the YOU survey also invited sampled students to join a panel so that the subsets of students who joined could answer follow-up surveys each half year for up to four years of their undergraduate study. When these data come to hand, they will allow us to reflect on the 2019 results reported above.

A second limitation of the present study is that our results are based on the student in-take of a single university only. While student and institutional characteristics are similar across the eight universities in a small country like New Zealand with a population of only 5.1 million or so, we cannot be sure that our results would not vary if a sample was drawn in the same way from one of the other institutions.

Thirdly, our results were designed to monitor the wellbeing of first year university students only and therefore we cannot generalise from the above results to students in the second, third or more levels of study.

Fourthly, we recognise but do not address the problem of shared or common method variance (CMV) which is inherent in self-report data—the spurious variance attributable to the errors present in self-reports (of wellbeing, physical and financial health in our case).²⁴

Conclusion

In most of the literature to date the wellbeing of students has been reported as a single number or index. What our study has shown is that underneath that single measure is a considerable heterogeneity of mood. From a university policy perspective therefore, it may not be sufficient to simply raise the mean level of wellbeing or its skew, but to also become aware of what is happening inside the index, the way in which the different components of wellbeing respond across students with different characteristics including their physical and financial health.

In this paper we have shown that the five components in the WHO-5 index have different distributions (Fig. 3), and that they respond differently to variations in the students’ physical and financial health (Figs. 4 and 5). The heterogeneity revealed by these two figures will remind university administrations that a ‘one size fits all’ response to low and falling wellbeing is unlikely to be uniformly felt within each student or across all students on campus. The corresponding implications for pastoral care, monitoring and interventions are particularly challenging because of this variety.

Appendices

Appendix 1. Estimates from the binary logistic model

The estimated effect on the log-odds of the selected models described in the text are reported below in Appendix Table 2. Baseline parameters with a 0 estimate are added for comparison purposes.

Table 2 Estimated log-odds of being Cheerful, Calm, Active, Rested and Interested more than half the time over the fortnight prior to the survey by student characteristic. Binary logistic GEE model

The probability of being ‘active’ more than half the time over the two weeks when the predictors (health, age, gender, and finance) are on the baseline is estimated as

$$\frac{{e}^{-0.75-1.13}}{1+{e}^{-0.75-1.13}}=0.13,$$

where -0.75 is the intercept. To calculate the probability, we can use this formula directly.

Similarly, the probability of being ‘cheerful’ more than half the time over the two weeks when the predictors (health, age, gender, and finance) are on the baseline is estimated as

$$\frac{{e}^{-0.75}}{1+{e}^{-0.75}}=0.32.$$

If we compare the ‘active’ vs. ‘cheerful’, the former is less than a half the latter.

The probability calculation in Fig. 4 in the text is derived in this way, given the conditions which define the particular panel, the health, sex and age of the student.

Appendix 2: Estimates from the ordinal logistic model

Table 3

Table 3 Estimated log-odds of being Cheerful, Calm, Active, Rested and Interested with different frequencies over the fortnight prior to the survey by student characteristic. An ordinal logistic model with proportional odds

Appendix 3. Visual Assessment of Proportional Odds Assumption

The method involves fitting five binary logistic models with different cut-off points, using one predictor at a time. If the lines for all predictors are parallel, as they are in our case, we conclude that the proportional odds assumption holds.

Fig. 6

Fig. 6

Visual assessment of the proportional odds assumption