The intervention takes the form of an interactive plush toy, designed to be handed over to the child and support in-the-moment soothing; see (Theofanopoulou et al 2019, Slovak et al 2018) for the design and data from previous deployments.

The toy is introduced to the child as an anxious creature that needs kind attention from humans. When picked up, the toy emits a frantic heartbeat that slows down if the child uses calm stroking movements. If the toy is soothed for long enough, it transitions into a purring vibration indicating a calm, content state.

Logic model underlying the intervention:

• Level 1: in-the-moment soothing support to children in emotional moments when they would attempt to calm down.
• Level 2: mechanisms that facilitate long-term engagement with the intervention, building on positive subjective experience of Level 1.
• Level 3: shift in children's ER practices and implicit beliefs about emotion, after repeated experience of Levels 1-2.

The investigators argue that a comparison with a non-active control-such as waiting list / treatment-as-usual (i.e., nothing)-would not allow us to distinguish the hypothesised impact on in-the-moment soothing of interactivity vs. the emergence of new family routines; and would be also open to unequal social desirability bias.

However, from the perspective of the hypothesised logic model (Levels 1-3), it is not necessary for the active control to have exactly the same form factor as the active toy, as long as it is comparable in size, shape, and appeal. In fact, the investigators have explicitly decided not to use deactivated Purrble units as active controls due to the increased risk of unblinding, whereby the participants search for or come across Purrble online (or notice the plastic enclosure with electronics inside the toy), and assume their unit is malfunctioning.

The objective of this study is to evaluate the impact of having access to the Purrble intervention, compared to an active control in the form of a non-interactive plush toy, on child daily emotion regulation (primary outcome) as well as a range of secondary outcomes over a period of one month.

The investigators hypothesise that engagement with an in-situ, 'bottom-up' emotion regulation intervention which enables in-the-moment soothing for children, will lead to measurable changes in child self-regulatory behaviours over time.

Composite end-of-day 4-item parent-report measure of the perceived child emotion regulation ability throughout the day. The composite score for each day will be computed as the mean value across the 4 items:

• Today, to what extent was the participant's child able to take difficult things in stride?
• Today, to what extent did the participant's child get easily triggered or upset?
• Today, to what extent was the participant's child able to calm down easily if upset?
• Today, to what extent did the participant's child get very emotional even after the littlest things?

These items were selected as tapping into the proximal emotion regulation behaviour that (a) would be affected if the intervention is effective, (b) directly observable by parents, (c) state-based to enable daily measurement, (d) connected to the intervention theory of change.

Measured by selected mDES (Fredrickson et al 2003) emotion triplets, balancing 2 negative and 2 positive sets, whilst being informed by prior qualitative studies. The items are listed below, all measured on a visual analogue scale with not at all and extremely as the anchors.

The investigators will collect semi-structured interview data with parents of up to 40% of the experimental group sample (20-25 families), and approximately 25% or the control group (15 families).

The investigators will be specifically aiming to recruit families who show the highest / lowest change in the outcome data over the primary period to qualitatively understand the potential moderators of intervention response for future research.

The semistructured interview guide will explore the engagement with the toy; any qualitative changes in child or family behaviour patterns that parents notice; appropriation (i.e., how the intervention ended up being used by different participants), and use trajectory over time.