Mood that lingers and mood that bounces back were not shown to be separate traits

Emotional inertia is the carryover of mood from one moment to the next. Recovery is how fast mood returns to a person's usual level after a sharp high or low. We asked whether these are two separate traits or one trait seen twice. In four open phone-survey datasets from the openESM database (71, 49, 99 and 259 eligible people), the two measures were computed on disjoint sets of prompt pairs and correlated across people. Across people, inertia and recovery were negatively correlated in all four datasets, r -0.44, -0.41, -0.28 and -0.29.c1 The coupling was weaker than a one-parameter AR(1) null in two datasets, 0008 clearly and 0018 by 0.001, and sat inside that null in the other two.c2 A factor model with two factors never fit better than one.c3 Split-half reliability ran from 0.03 to 0.47, so the factor test had little power.c4 The preregistered prediction that the two are separate was not supported in any dataset on both of its tests. We report it as an honest nullDefinition: honest null research method (our usage) A working test that found no effect beyond a stated bound, a forecast that failed, or an error of our own found and fixed, reported with the same weight as a positive result. Excludes a void run, and a result left unpublished because it was negative. full definition with low power, and with one methods warning: with the usual all-pairs inertia, which reuses the spike pairs, the correlation reached 0.67 to 0.81 in size.c5

Emotional inertiaDefinition: emotional inertia affective science How far a person's mood at one prompt predicts their mood at the next, measured as the lag-one correlation of their own mood series. Excludes average mood, how much mood varies, and any claim about what causes the carryover. full definition was introduced as a person-level property by Kuppens, Allen and Sheeber [2], who found higher inertia of both positive and negative emotions in people with depression and low self-esteem, across two naturalistic studies. Inertia is usually read off as an autocorrelation, so it measures how self-predictable a person's mood is from one prompt to the next.

Koval and colleagues [3] asked how inertia relates to the events people meet. In 200 first-year students, measured in daily life and in a film-clip task, the most consistent result was that higher inertia of negative affect went with slower recovery after negative stimuli. Their abstract reads this as inertia being driven mostly by weaker repair of mood after negative events. Schreuder and colleagues [5] measured recovery more directly: in a preregistered study of 68 adults with burst sampling, they timed returns to baseline after positive and negative episodes with survival analysis, and trait resilience did not predict return time.

A broader caution comes from Dejonckheere and colleagues [4]. Across many datasets, measures of mood dynamics such as autocorrelation added little to the prediction of well-being once mean affect and its variability were known. A dynamic measure has to earn its place as a separate quantity.

Our question sits between these. If inertia and recovery are two traits, they should vary across people more loosely than a model with one parameter would allow. If they are one trait, the coupling should look like what a single parameter produces on the same prompt schedules. The search we ran found adjacent work but no test of this form; that is what the search returned, not proof that none exists.

The preregistrationDefinition: preregistration research method (metascience) A dated written plan for a study, fixed and hash-locked before any result is seen: the question, the data, the statistic, the controls, the forecasts and the kill conditions. Excludes a plan revised after looking at the outcome, and a protocol written only for the record after the run. full definition was written on 29 October 2026, before any inertia, recovery, correlation or factor model was computed on the real data. Before writing it we had seen column names, row counts, the most common raw values of each mood column, and the number of prompts per person. All design choices were tested on synthetic populations first.

The idea and the prediction came from the author, who framed mood as an audio chain: a reverb, how long a feeling rings on, and a compressor release, how fast a large swing returns. The prediction had two parts, tested in each dataset separately:

The verdictDefinition: verdict research method (our usage) The pass or fail of one preregistered rule set against the run's numbers, read off by code. Excludes an interpretation written after reading the numbers. full definition rules were fixed in advance. A dataset is "supported" when the shuffle check P0, P1 and P2 all pass; "partly" when P0 passes and exactly one of P1 and P2; "null" when P0 passes and both fail; "instrument failure" when P0 fails; "untestable" with fewer than 30 eligible people. There was no pooling across datasets, because their scales and samples differ. The preregistration's SHA-256 is given in the reproduction section.

The four datasets come from openESM [1], a database of open experience samplingDefinition: experience sampling psychology (methods) A study design in which people answer short questions on a phone several times a day, so that mood is recorded close to the moment it is felt. Excludes one-off questionnaires and recall of past weeks. full definition data, all under the Creative Commons Attribution 4.0 licence (CC BY 4.0). Only group statistics are reported here; nothing describes an individual participant.

The four input files were hashed by the run, and the hashes are in its result file. The samples are convenience samples, each on its own scale, which is why each is analysed alone.

A lag pairDefinition: lag pair time-series analysis Two adjacent prompts on the same study day, the earlier one called the lead. A missed prompt or a night breaks the pair. Excludes pairs that cross a night or skip a prompt. full definition is two adjacent prompts on the same study day. For a person with mean $m$ and standard deviation $s$ over all their valid prompts, the deviation at prompt $t$ is

A spikeDefinition: spike our usage A lead prompt whose mood sits at least 1.5 of the person's own standard deviations from the person's own mean. Excludes deviations judged against other people or against a population norm. full definition is the lead prompt of a lag pair with a deviation of at least $1.5s$ in size. For each spike, the share of the deviation that has gone at the next prompt is

clipped to the range -1 to 2. A person's recoveryDefinition: recovery affective science (our operational form) The median, over a person's spikes, of the share of each spike's distance from the person's mean that has gone by the next prompt, with 1 meaning back at the mean and 0 meaning no change. Excludes recovery measured in clock time, and recovery after events that did not produce a spike. full definition is the median of $u_t$ over their spikes, so 1 means back at the mean one prompt later and 0 means no change.

Primary inertia is the Pearson rDefinition: Pearson r statistics The correlation coefficient between two quantities measured on the same units, from -1 through 0 for no linear relation to 1. Excludes non-linear relations and any statement about cause. full definition between $x_t$ and $x_{t+1}$ over the lag pairs whose lead prompt is not a spike. The reason was settled on synthetic data before the run. Inertia over all pairs is dominated by large deviations, so it reads the same spike pairs that define recovery. In a synthetic population with separate rates for small and large deviations, all-pairs inertia still correlated with recovery at -0.77 to -0.83; the disjoint version gave -0.23 to -0.29, against -0.54 to -0.61 in a one-parameter population. All-pairs inertia was kept as a secondary measure.

A person was eligible with at least 30 valid prompts, 20 lag pairs, 15 non-spike pairs and 5 spikes. A dataset was tested with at least 30 eligible people.

For each dataset, $r$ is the Pearson correlation of inertia and recovery across eligible people. Its 95 percent interval is a person bootstrapDefinition: person bootstrap statistics (resampling) An interval found by drawing people with replacement many times, recomputing the statistic each time, and taking the middle of the resulting spread. Excludes resampling of single prompts, which would treat one person's prompts as independent. full definition with 2,000 resamples.

The decisive comparison is with an AR(1) processDefinition: AR(1) process time-series statistics A series in which each value is the mean plus a fixed fraction of the previous value's distance from the mean, plus fresh random noise. The fraction is the single parameter. Excludes models with separate rates for small and large deviations, and models with measurement noise on top. full definition, in which each person has a single parameter $\varphi$:

where $ϵ$ is fresh Gaussian noise. Each eligible person is simulated on their exact prompt schedule, with the same days, prompts and missed prompts, a fresh stationary start each day, their own $m$ and $s$, and values rounded and clipped to the scale. The person's $\varphi$ is their all-pairs inertia corrected for short-series Kendall biasDefinition: Kendall bias time-series statistics The downward bias of a lag-one correlation estimated from a short series, about (1 + 3 phi)/n for a series of n values with true value phi (Kendall 1954). Excludes bias from measurement noise, which is a separate attenuation. full definition,

with $n$ the number of pairs, then shrunk toward the dataset mean so that its spread excludes sampling noise, and clipped to -0.5 to 0.95. The whole pipeline is rerun on the simulated people, and the size of $r$ is recorded. Two hundred draws give the null distributionDefinition: null distribution statistics The spread of scores a control gives over many random draws. Its 95th percentile is the bar a real score must clear. Excludes a theoretical distribution assumed rather than drawn from the data. full definition.

Each person gives four indicators: inertia and recovery computed on odd study days and on even study days, each half needing at least 10 non-spike pairs and 3 spikes. A one-factor modelDefinition: factor model psychometrics (confirmatory factor analysis) A model that explains the correlations among several measured indicators by a smaller number of unseen common factors, fitted by maximum likelihood. Excludes exploratory searches for the number of factors, and models of change over time. full definition (four loadings, four unique variances, 2 degrees of freedom) is compared with a two-factor model with inertia halves on one factor, recovery halves on the other and a free factor correlation (1 degree of freedom). The two-factor model wins only if the chi-square difference has p below 0.05 and its BICDefinition: BIC statistics (model selection) The Bayesian information criterion, a fit score that charges each extra parameter a penalty growing with sample size. The lower value is preferred. Excludes a test of whether either model is true. full definition is lower. The one-factor model is the two-factor model with the factor correlation at plus or minus 1, a boundary value, so the 1-degree-of-freedom p is conservative. The same halves give each measure's split-half reliabilityDefinition: split-half reliability psychometrics The correlation across people between a measure computed on one half of each person's data and the same measure on the other half. Here the halves are odd and even study days. Excludes test-retest reliability over months, and the validity of the measure. full definition.

Each control's p value is the share of draws at or above the real value, with one added to the count and the number of draws:

At 200 draws the smallest value is 0.005.

Three controlsDefinition: control statistics and experimental design A version of the data with the structure under test removed (for example shuffled or pooled), scored the same way as the real data, so the real score has something to beat. Excludes a comparison with a different dataset or with a published number. full definition ran per dataset, 200 draws each, from one random generator with seed 20261029.

The AR(1) null was itself a planted checkDefinition: planted check research method; called a positive control in experimental science Data built so that the right answer is known, run through the same analysis before the real data, to show that the analysis can see the effect when it is there. Excludes any check made on the real data, which cannot show what the analysis misses. full definition before the run. In a synthetic one-parameter world the observed correlation fell inside this null in 6 of 6 runs, and in a two-parameter world below its 5th percentile in 6 of 6 runs,c6 on both continuous and 5-point scales. So the null can tell the two worlds apart when the data are as clean as the simulation.

The shuffle check passed in all four datasets. Mean primary inertia was 0.236, 0.404, 0.270 and 0.162, against shuffle 95th percentiles of 0.013, 0.011, 0.013 and 0.000, each with p 0.005, the smallest value 200 draws allow.

Table 1 gives the main numbers. Across people, inertia and recovery were negatively correlated in all four datasets, r -0.44, -0.41, -0.28 and -0.29.c1 Each 95% intervalDefinition: 95% interval statistics The range that holds the middle 95 percent of the bootstrap or control draws for a number. We report it beside the number. Excludes a statement that the true value lies inside with 95 percent probability. full definition excludes 0 and lies inside -0.7 to 0.7. People whose mood carries over more tend to recover less of a spike by the next prompt.

The coupling was weaker than a one-parameter AR(1) null in two datasets, 0008 clearly and 0018 by 0.001, and sat inside that null in the other two.c2 In 0008 the size of $r$ was 0.279 against a null 5th percentile of 0.367. In 0018 it was 0.4391 against 0.4399, a pass that a different seed could reverse. In 0062 it was 0.414 inside a null running from 0.215 to 0.682, and in 0076 it was 0.289, next to the null mean of 0.283. Figure 1 draws these against the null and beside the all-pairs value.

A factor model with two factors never fit better than one.c3 In 0018 (53 people with both halves) the chi-square difference was 0.055 with p 0.81 and the BIC favoured one factor by 3.9; the factor correlation was 0.95. In 0008 (60 people) the difference was 0.001 with p 0.97, BIC +4.1, factor correlation 0.98. In 0076 (152 people) the difference was 0.00 with p 1.0, BIC +5.0, and the factor correlation sat at the boundary, -1.00. In 0062 only 5 people had enough spikes on both odd and even days, because the study ran in two 7-day bursts, so the model could not be fitted.

Split-half reliability ran from 0.03 to 0.47, so the factor test had little power.c4 For inertia it was 0.38, 0.47 and 0.03 in 0018, 0008 and 0076; for recovery 0.33, 0.11 and 0.17. Two factors cannot separate when each indicator carries this much noise.

The definition of inertia matters more than any other choice. With the usual all-pairs inertia, which reuses the spike pairs, the correlation reached 0.67 to 0.81 in size.c5 The values were -0.81, -0.75, -0.67 and -0.69. Under that definition P1 would have failed in every dataset on its first condition. Other preregistered sensitivity checks changed no conclusion: Kendall-corrected inertia gave r -0.43, -0.42, -0.28 and -0.29, and a spike threshold of 1.0 standard deviations gave -0.37, -0.32, -0.27 and -0.16 with more people eligible (79, 138, 112 and 272).

Coupling grew with series length in three datasets (Figure 2). Split by prompts per person into thirds, $r$ ran -0.14, -0.45 and -0.78 in 0018, -0.19, -0.27 and -0.40 in 0008, and -0.25, -0.24 and -0.37 in 0076. In 0062 it ran -0.31, -0.78 and +0.25 with 13 to 19 people per third. This pattern fits attenuationDefinition: attenuation psychometrics The shrinking of an observed correlation toward zero when the measures that enter it are noisy. Excludes a true weak relation between the underlying quantities. full definition: in short series both measures are noisy and the correlation shrinks toward zero. The thirds are small and have no intervals. The 40-prompt control C3 was usable only in 0076, where the mean size of $r$ was 0.235 (5th to 95th percentile 0.104 to 0.370); in the other three, too few people stayed eligible in 40 prompts.

Table 2 sets the forecasts written in the preregistration against the outcomes.

Read by the preregistered rules, 0018 and 0008 are "partly" (P1 passed, P2 failed), 0076 is "null", and 0062 failed P1 with P2 untestable. No dataset supported both parts of the prediction. The headline is therefore that inertia and recovery were not shown to be separate traits.

That does not show they are one trait, and two features of the design lean toward a pass rather than a fail. The AR(1) null has no measurement-noise term. Noise in the real data weakens the observed coupling, which makes a real value below the null's 5th percentile easier to reach. The two P1 passes are weak evidence for that reason, and the 0018 pass sits at the edge. The factor test, on the other side, had too little reliability to detect two factors even if they exist.

The direction agrees with Koval and colleagues [3], whose abstract reports higher negative-affect inertia going with slower recovery. It also fits the caution of Dejonckheere and colleagues [4]: a dynamic measure computed from few prompts carries little information of its own, and here two such measures could not be told apart. Recovery measured in clock time with dense sampling, as in Schreuder and colleagues [5], is a better instrument for the question than one-prompt-later recovery from five or six prompts a day.

The methods result stands apart from the null. Inertia computed over all pairs shares data with recovery, and in these four datasets that overlap alone moves the size of the correlation from 0.28 to 0.44 up to 0.67 to 0.81. Any study that relates autocorrelation to recovery after peaks should compute them from disjoint pairs, or report how much of the link the overlap creates.