What elements help predict if students run a bigger risk of mental health problems?

This graph gives an answer:

The graph is taken from a study on UK students aged 12 to 21.

From the press release:

A new study published in JCPP Advances has compared the wellbeing of UK students who remained at home for schooling during the first lockdown period of the COVID-19 pandemic with those who accessed school in person.

In the study, which included 11,765 students in grades 8-13 (aged 12-21 years), females, students who had experienced food poverty, and those who had previously accessed mental health support were at greatest risk of depression, anxiety, and a deterioration in wellbeing. Students who accessed in-person schooling had poorer mental health, but this was accounted for by their different characteristics and background circumstances.

“Identifying circumstances that could make some school pupils especially vulnerable during lockdowns is important, both for allocating limited in-school places and for effectively supporting their education and wellbeing,” said lead author Karen L. Mansfield, PhD, of the University of Oxford, in the UK. “We managed to capture responses from a diverse group of pupils during the first UK partial school closure period, and our results highlighted established risk factors as well as other circumstances of heightened relevance during lockdown that were related to pupils’ mental health and wellbeing.”

Abstract of the study:

Background
Understanding adolescents’ mental health during lockdown and identifying those most at risk is an urgent public health challenge. This study surveyed school pupils across Southern England during the first COVID-19 school lockdown to investigate situational factors associated with mental health difficulties and how they relate to pupils’ access to in-school educational provision.

Methods
A total of 11,765 pupils in years 8–13 completed a survey in June–July 2020, including questions on mental health, risk indicators and access to school provision. Pupils at home were compared to those accessing in-school provision on risk and contextual factors and mental health outcomes. Multilevel logistic regression analyses compared the effect of eight risk and contextual factors, including access to in-school provision, on depression, anxiety and self-reported deterioration in mental wellbeing.

Results
Females, pupils who had experienced food poverty and those who had previously accessed mental health support were at greatest risk of depression, anxiety and a deterioration in wellbeing. Pupils whose parents were going out to work and those preparing for national examinations in the subsequent school year were also at increased risk. Pupils accessing in-school provision had poorer mental health, but this was accounted for by the background risk and contextual factors assessed, in line with the allocation of in-school places to more vulnerable pupils.

Conclusions
Although the strongest associations with poor mental health during school closures were established risk factors, further contextual factors of particular relevance during lockdown had negative impacts on wellbeing. Identifying those pupils at greatest risk for poor outcomes is critical for ensuring that appropriate educational and social support can be given to pupils either at home or in-school during subsequent lockdowns.