COGS 589 Final Project
Damlanur Kırarslan
2023-06-08
Interplay of Emotional Regulation Strategies and Feedback in Predicting Task Performance and Mood: A Mixed Model Analysis
1. Introduction
In this project, data collected for the PSY 304 Experimental Psychology course will be examined. For the course mentioned, the researchers aimed to investigate how different emotion regulation strategies (reappraisal and suppression) affect the performance and mood of the participants depending on the feedback type (absolute and relative) and feedback level (positive and negative). By exploring the impact of different emotion regulation techniques on performance and mood, and how feedback type and level influence them, the researchers hoped to gain insights into the complex interplay between emotions, cognition, and action.
2. Background
There are two main emotion regulation strategies measured to understand the effect of emotion regulation on the performance. These are cognitive reappraisal and emotion suppression. These two differ on the stage of emotion generation they are implemented. According to Gross (2001) cognitive reappraisal happens at the beginning of emotion generation and suppression happens at the end of emotion generation. Cognitive reappraisal, changes the impacts of stimuli to change the meaning of the situation for the person (Gross, 2001) Suppression on the other hand concerns the expressions of the emotions. People do not change their emotions, but they change how they express it, therefore, it happens at the late stages of the emotion generation process (Gross, 2001). The figure below describes the process.
Emotion regulation strategies known to have an effect on the performance in cognitive tasks. According to Gross (2001), suppression expends cognitive resources, because it requires continuous self-monitoring and self-suppression. As a result, cognitive performance is decreased because of the cognitively taxing emotion regulation strategy. Reappraisal on the other hand, does not involve such processes, therefore it is not cognitively taxing. As a result, people who use cognitive reappraisal strategy are more likely to have better cognitive performance.
Additionally, feedback is an important emotion causing event. According to Goetz and colleagues (2018), associations between positive emotion and positive feedback, negative emotion and negative feedback are demonstrated by many empirical findings. Therefore, people’s responses to feedback in the form of regulation can be an important indication of performance. The study conducted by Raftery and Bizer investigated the relationship between feedback on a given task and emotion regulation, where the results revealed that among reappraises, those who received negative feedback performed better on the second task (2009). Moreover, feedback can also come in different forms. Our interest is in absolute and relative feedback. Absolute feedback is direct feedback on the performance in a task. Comparative feedback on the other hand, compares performance with other people. It is argued that people make sense of their performance based on comparisons with other people’s performance (Festinger, 1954 as cited in, Moore & Klein, 2008). Moore and Klein (2008) found that absolute standing feedback had a greater impact than relative standing feedback on participants’ affective responses and their performance. However, there are not many studies on how people with different emotion regulation strategies respond to such feedback and how their performance is affected. This is one of the main aims of our study.
Feedback also has an effect on the mood. Gross and John (2003) found that emotional suppression strategies resulted in prolonged periods of negative affect because of people’s tendency to fixate on them. On the other hand, they claimed that the reappraises experience and express more positive emotions and less negative ones (Gross & John, 2003). This can result in a difference of mood during the task.
3. Aim of the Study
In the current study, the researchers looked into how the social standing and valence of the feedback would affect the performance and mood of people using various emotion regulation strategies.
library(readr)
wide_data <- "https://docs.google.com/spreadsheets/d/e/2PACX-1vSjgwQL54ZA8h9PjQ7Nl4mtodlU5RjZ99K_XFzJ5nmLWGeArvMmonSWOev7b1UhdeA73ilgkn5_pKBf/pub?gid=0&single=true&output=csv"
wide_data <- read_csv(url(wide_data))## Rows: 60 Columns: 40
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Gender
## dbl (39): ID, feedback_type, feedback_valence, Mood_1, Mood_2, Performance_1...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.wide_data## # A tibble: 60 × 40
## ID feedback_type feedback_valence Mood_1 Mood_2 Performance_1
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 3 1 28 26 28
## 2 2 4 2 43 43 66
## 3 3 4 1 47 38 91
## 4 4 4 1 47 43 45
## 5 5 4 2 34 35 64
## 6 6 3 2 39 39 16
## 7 7 3 1 51 52 74
## 8 8 4 1 50 48 42
## 9 9 3 1 47 49 20
## 10 10 3 2 52 51 78
## # ℹ 50 more rows
## # ℹ 34 more variables: Performance_2 <dbl>, ERS <dbl>, Q3_1 <dbl>, Q3_2 <dbl>,
## # Q3_3 <dbl>, Q3_4 <dbl>, Q3_5 <dbl>, Q3_6 <dbl>, Q3_7 <dbl>, Q3_8 <dbl>,
## # Q3_9 <dbl>, Q3_10 <dbl>, A1_1 <dbl>, A1_2 <dbl>, A1_3 <dbl>, A1_4 <dbl>,
## # A1_5 <dbl>, A1_6 <dbl>, A1_7 <dbl>, A1_8 <dbl>, A1_9 <dbl>, A1_10 <dbl>,
## # A2_1 <dbl>, A2_2 <dbl>, A2_3 <dbl>, A2_4 <dbl>, A2_5 <dbl>, A2_6 <dbl>,
## # A2_7 <dbl>, A2_8 <dbl>, A2_9 <dbl>, A2_10 <dbl>, Age <dbl>, Gender <chr>This data consists of responses to the Emotion Regulation questionnarie (Q3_1, Q3_2…) and number of words solved in the first (A1_1, A1_2…) and the second (A2_1, A2_2…) anagram tasks. Also the data depicts fedback type, feedback valence, cumulative scores for each mood questionnaires conducted before and after the feedback condition. Lastly, the descriptives such as age and gender are also included in the data.
colnames(wide_data)## [1] "ID" "feedback_type" "feedback_valence" "Mood_1"
## [5] "Mood_2" "Performance_1" "Performance_2" "ERS"
## [9] "Q3_1" "Q3_2" "Q3_3" "Q3_4"
## [13] "Q3_5" "Q3_6" "Q3_7" "Q3_8"
## [17] "Q3_9" "Q3_10" "A1_1" "A1_2"
## [21] "A1_3" "A1_4" "A1_5" "A1_6"
## [25] "A1_7" "A1_8" "A1_9" "A1_10"
## [29] "A2_1" "A2_2" "A2_3" "A2_4"
## [33] "A2_5" "A2_6" "A2_7" "A2_8"
## [37] "A2_9" "A2_10" "Age" "Gender"In this study, it is hypothesised that among reappraisers who receive negative feedback with relative standing would have better performance and a higher mood as opposed to reappraisers who receive negative feedback with absolute standing and to suppressors who receive negative feedback with relative and absolute standing. Moreover, in the second hypothesis it is stated that suppressors who receive negative feedback regardless of the feedback type will show poorer performance in the second task and express less positive affect relative to suppressors who receive relative positive feedback.
The valence of the feedback, feedback type and emotion regulation strategy were the independent variables of the study, while each has two levels. For the feedback valence, the levels are referred as absolute and relative, for the feedback type they are negative and positive. And lastly for the emotion regulation strategy, they are named as suppression and reappraisal. Mood change and performance change between the anagram tasks are the dependent variable of the study.
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(psych)
# transforming Gender variable into a factor
wide_data$Gender <- as.factor(wide_data$Gender)
# calculating the mean and standard deviation of age, grouped by gender
descriptive_stats <- wide_data %>%
group_by(Gender) %>%
summarise(Mean_Age = mean(Age, na.rm = TRUE),
SD_Age = sd(Age, na.rm = TRUE))
print(descriptive_stats)## # A tibble: 3 × 3
## Gender Mean_Age SD_Age
## <fct> <dbl> <dbl>
## 1 Female 20.2 1.19
## 2 Male 22.1 3.01
## 3 <NA> NaN NA4. Preparatory Work
I started the data cleaning and transformig the data into long format by calculating the overall scores of the questionnaries. I calculated the Emotion Regulation scores by averaging the scores for the questions related to “reappraisal” and “suppression” seperately. Mean_Reappraisal, Mean_Suppression, and ERS. Then, I converted the ERS column from character to factor, then to numeric.
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.2 ✔ tibble 3.2.1
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ ggplot2::%+%() masks psych::%+%()
## ✖ ggplot2::alpha() masks psych::alpha()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(dplyr)
library(tidyr)
wide_data <- wide_data %>%
mutate(
Mean_Reappraisal = rowMeans(select(., Q3_1, Q3_3, Q3_5, Q3_7, Q3_8, Q3_10), na.rm = TRUE),
Mean_Suppression = rowMeans(select(., Q3_2, Q3_4, Q3_6, Q3_9), na.rm = TRUE)
) %>%
mutate(
ERS = ifelse(Mean_Reappraisal - Mean_Suppression > 0, "R", "S")
)
wide_data$ERS <- as.numeric(factor(wide_data$ERS, levels = c("R", "S")))For the performance variable, I adapted column names as Anagram_Before and Anagram_After. Then, I calculated the average performance for the anagram tasks before and after the feedback condition.
Perf_1_cols <- paste0("A1_", 1:10)
Perf_2_cols <- paste0("A2_", 1:10)
wide_data <- wide_data %>%
mutate(
Perf_1 = rowMeans(select(., all_of(Perf_1_cols)), na.rm = TRUE),
Perf_2 = rowMeans(select(., all_of(Perf_2_cols)), na.rm = TRUE)
) #The mood change and the performance change are calculated.
wide_data$Mood_change <- wide_data$Mood_2 - wide_data$Mood_1
wide_data$Perf_change <- wide_data$Perf_2 - wide_data$Perf_1I have detected outliers with z-scores of performance and mood variable for each participant, then I removed the outliers.
wide_data$Mood_change_z <- as.vector(wide_data$Mood_change)
wide_data$Perf_change_z <- as.vector(wide_data$Perf_change)
wide_data <- wide_data %>%
filter(Mood_change_z > -2.5 & Mood_change_z < 2.5) %>%
filter(Perf_change_z > -2.5 & Perf_change_z < 2.5)Lastly, I transformed the data into the long format data frame and kept only the necessary columns. After that, I converted ERS, feedback_type, feedback_valence into factor.
long_data <- wide_data %>%
pivot_longer(
cols = c(Mood_1:Mood_2, Perf_1:Perf_2),
names_to = c(".value", "Time"),
names_pattern = "(Mood|Perf)_(.*)"
)
long_data <- long_data %>%
select(ID, Age, Gender, feedback_type, feedback_valence, ERS, Mood, Perf)
long_data## # A tibble: 68 × 8
## ID Age Gender feedback_type feedback_valence ERS Mood Perf
## <dbl> <dbl> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 21 Female 3 1 1 28 2.8
## 2 1 21 Female 3 1 1 26 3.5
## 3 2 21 Female 4 2 1 43 6.6
## 4 2 21 Female 4 2 1 43 8.2
## 5 5 34 Male 4 2 1 34 6.4
## 6 5 34 Male 4 2 1 35 5.9
## 7 6 22 Male 3 2 1 39 1.6
## 8 6 22 Male 3 2 1 39 2.2
## 9 7 21 Male 3 1 1 51 7.4
## 10 7 21 Male 3 1 1 52 5.9
## # ℹ 58 more rowslong_data$ERS <- factor(long_data$ERS,
levels = c(1, 2),
labels = c("Reappraisal", "Suppression"))
long_data$feedback_type <- factor(long_data$feedback_type,
levels = c(3, 4),
labels = c("Absolute", "Relative"))
long_data$feedback_valence <- factor(long_data$feedback_valence,
levels = c(1, 2),
labels = c("Negative", "Positive"))5. Data Analysis
I analysed the effect of ERS and feedback type and valence on performance and mood seperately in liear mixed model analysis. For the analysis of the “mood” variable, my outcome variable is Mood, my predictors are ERS, feedback_type, and feedback_valence, and the grouping variable is ID. The following model includes all the predictors (ERS, feedback_type, and feedback_valence) and their interactions (Time * ERS * feedback_type * feedback_valence), along with a random intercept for each individual (ID).
library(lme4)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpacklibrary(lmerTest)##
## Attaching package: 'lmerTest'## The following object is masked from 'package:lme4':
##
## lmer## The following object is masked from 'package:stats':
##
## stepmood_model <- lmer(Mood ~ ERS * feedback_type * feedback_valence + (1 | ID), data = long_data, REML = FALSE)
summary(mood_model)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: Mood ~ ERS * feedback_type * feedback_valence + (1 | ID)
## Data: long_data
##
## AIC BIC logLik deviance df.resid
## 379.0 401.2 -179.5 359.0 58
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.14956 -0.55293 -0.00502 0.53691 1.17115
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 75.6597 8.6983
## Residual 0.8676 0.9315
## Number of obs: 68, groups: ID, 34
##
## Fixed effects:
## Estimate
## (Intercept) 39.41667
## ERSSuppression 0.08333
## feedback_typeRelative 0.16667
## feedback_valencePositive -3.66667
## ERSSuppression:feedback_typeRelative -3.83333
## ERSSuppression:feedback_valencePositive 0.66667
## feedback_typeRelative:feedback_valencePositive 7.13889
## ERSSuppression:feedback_typeRelative:feedback_valencePositive -7.72222
## Std. Error
## (Intercept) 3.56122
## ERSSuppression 9.42209
## feedback_typeRelative 5.03632
## feedback_valencePositive 5.63078
## ERSSuppression:feedback_typeRelative 11.26155
## ERSSuppression:feedback_valencePositive 11.53966
## feedback_typeRelative:feedback_valencePositive 7.26930
## ERSSuppression:feedback_typeRelative:feedback_valencePositive 14.75507
## df t value
## (Intercept) 34.00000 11.068
## ERSSuppression 34.00000 0.009
## feedback_typeRelative 34.00000 0.033
## feedback_valencePositive 34.00000 -0.651
## ERSSuppression:feedback_typeRelative 34.00000 -0.340
## ERSSuppression:feedback_valencePositive 34.00000 0.058
## feedback_typeRelative:feedback_valencePositive 34.00000 0.982
## ERSSuppression:feedback_typeRelative:feedback_valencePositive 34.00000 -0.523
## Pr(>|t|)
## (Intercept) 8.15e-13 ***
## ERSSuppression 0.993
## feedback_typeRelative 0.974
## feedback_valencePositive 0.519
## ERSSuppression:feedback_typeRelative 0.736
## ERSSuppression:feedback_valencePositive 0.954
## feedback_typeRelative:feedback_valencePositive 0.333
## ERSSuppression:feedback_typeRelative:feedback_valencePositive 0.604
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ERSSpp fdbc_R fdbc_P ERSSp:_R ERSS:_P f_R:_P
## ERSSupprssn -0.378
## fdbck_typRl -0.707 0.267
## fdbck_vlncP -0.632 0.239 0.447
## ERSSpprs:_R 0.316 -0.837 -0.447 -0.200
## ERSSpprs:_P 0.309 -0.816 -0.218 -0.488 0.683
## fdbck_tR:_P 0.490 -0.185 -0.693 -0.775 0.310 0.378
## ERSSp:_R:_P -0.241 0.639 0.341 0.382 -0.763 -0.782 -0.493fixef(mood_model)## (Intercept)
## 39.41666667
## ERSSuppression
## 0.08333333
## feedback_typeRelative
## 0.16666667
## feedback_valencePositive
## -3.66666667
## ERSSuppression:feedback_typeRelative
## -3.83333333
## ERSSuppression:feedback_valencePositive
## 0.66666667
## feedback_typeRelative:feedback_valencePositive
## 7.13888889
## ERSSuppression:feedback_typeRelative:feedback_valencePositive
## -7.72222222ranef_mood <- ranef(mood_model)$ID
ranef_mood## (Intercept)
## 1 -1.234588e+01
## 2 -5.523882e-02
## 5 -8.506779e+00
## 6 3.231471e+00
## 7 1.201444e+01
## 8 9.362980e+00
## 9 8.534398e+00
## 10 1.491448e+01
## 12 6.545801e+00
## 13 -4.805778e+00
## 14 -3.535285e+00
## 16 -2.320031e+00
## 19 -8.285823e-02
## 21 8.285823e-02
## 22 -9.197264e+00
## 23 -8.009629e+00
## 24 7.125808e+00
## 26 -1.483162e+01
## 28 -4.722919e+00
## 29 -1.099253e+01
## 33 -1.740023e+00
## 35 2.927658e+00
## 37 7.705816e+00
## 38 -1.798024e+01
## 39 1.585354e+01
## 40 1.582592e+01
## 41 -7.457241e+00
## 42 -5.551502e+00
## 45 3.921956e+00
## 49 8.396301e+00
## 52 -1.574306e+00
## 53 -7.457241e+00
## 55 4.722919e+00
## 59 -3.061081e-12The linear mixed model was used to predict Mood based on the three predictors: ERS, feedback type, and feedback valence. The model also accounted for the random effects of the individual participants (ID). The overall model fit is represented by the AIC and BIC values. Lower values for both AIC and BIC suggest a better fit. The AIC of the model is 379.0, and the BIC is 401.2. The fixed effects table provides the estimates, standard errors, degrees of freedom, t values, and p values for each predictor and their interactions. The intercept, which is the predicted Mood score when all predictors are at their reference levels, is 39.42, and it is highly significant (p < 0.001). The main effects of ERS Suppression, feedback type relative, and feedback valence positive are not significant (p > 0.05). The interaction effects among ERS suppression, feedback type relative, and feedback valence positive are also not significant (p > 0.05). The correlation of fixed effects provides an overview of the correlations between the estimated effects.
ggplot(long_data, aes(x=interaction(feedback_type, feedback_valence), y=Mood, fill=factor(ERS))) +
geom_boxplot() +
scale_fill_manual(values = c("Suppression" = "orange", "Reappraisal" = "purple"),
name = "Emotion Regulation Strategy",
labels = c("Suppression", "Reappraisal")) +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
labs(x="Interaction of Feedback Type and Valence",
y="Mood",
title="Interaction of Feedback Type and Valence on Mood")
However, as seen in the plot, this model did not find significant
effects of ERS strategy, feedback type, and feedback valence on Mood.
Other variables not included in the model may have an impact on Mood,
and further analysis could be beneficial.
From the p-values in the fixed effects table, it appears that none of the effects or interactions are statistically significant except for the intercept. Then individual-level intercepts were examined to understand how much mood varies by individual when all other variables are held constant.
The necessary assumptions checks were done related with the mood variable to ensure the results of the analysis. First the independence of the residuals were investigated. For mixed models, this refers to the independence of residuals within groups (random effects). You can visually inspect this with a residuals vs fitted plot, where you should not see any obvious pattern.
resid <- residuals(mood_model)
fitted <- fitted(mood_model)
plot(fitted, resid, main = "Residuals vs Fitted", xlab = "Fitted values", ylab = "Residuals")
abline(h = 0, col = "red")
Then nomrality assumption were checked by the Q-Q plot of the residuals
and the Shapiro Wilk test. A low p-value (usually < 0.05) indicates
that the null hypothesis can be rejected and the data do not follow a
normal distribution.
qqnorm(resid)
qqline(resid)
shapiro.test(resid)##
## Shapiro-Wilk normality test
##
## data: resid
## W = 0.93672, p-value = 0.001859Lastly, to check homogeneity of variance across levels of a factor (like feedback type, for example), a boxplot was formed
boxplot(split(resid, long_data$feedback_type), main = "Residuals by feedback type", xlab = "Feedback type", ylab = "Residuals")
For the analysis of the “performance” variable, the outcome variable is Performance, the predictors are ERS, feedback_type, and feedback_valence, and the grouping variable is ID. The following model includes all the predictors (ERS, feedback_type, and feedback_valence) and their interactions (Time * ERS * feedback_type * feedback_valence), along with a random intercept for each individual (ID).
perf_model <- lmer(Perf ~ ERS * feedback_type * feedback_valence + (1 | ID), data = long_data, REML = FALSE)
summary(perf_model)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: Perf ~ ERS * feedback_type * feedback_valence + (1 | ID)
## Data: long_data
##
## AIC BIC logLik deviance df.resid
## 269.6 291.8 -124.8 249.6 58
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.5438 -0.6220 0.0479 0.5201 1.4702
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 3.6717 1.9162
## Residual 0.6609 0.8129
## Number of obs: 68, groups: ID, 34
##
## Fixed effects:
## Estimate
## (Intercept) 4.9583
## ERSSuppression 2.2917
## feedback_typeRelative -0.7167
## feedback_valencePositive 0.3792
## ERSSuppression:feedback_typeRelative -0.8500
## ERSSuppression:feedback_valencePositive -2.7292
## feedback_typeRelative:feedback_valencePositive 0.4458
## ERSSuppression:feedback_typeRelative:feedback_valencePositive 2.4958
## Std. Error
## (Intercept) 0.8167
## ERSSuppression 2.1608
## feedback_typeRelative 1.1550
## feedback_valencePositive 1.2913
## ERSSuppression:feedback_typeRelative 2.5827
## ERSSuppression:feedback_valencePositive 2.6465
## feedback_typeRelative:feedback_valencePositive 1.6671
## ERSSuppression:feedback_typeRelative:feedback_valencePositive 3.3839
## df t value
## (Intercept) 34.0000 6.071
## ERSSuppression 34.0000 1.061
## feedback_typeRelative 34.0000 -0.620
## feedback_valencePositive 34.0000 0.294
## ERSSuppression:feedback_typeRelative 34.0000 -0.329
## ERSSuppression:feedback_valencePositive 34.0000 -1.031
## feedback_typeRelative:feedback_valencePositive 34.0000 0.267
## ERSSuppression:feedback_typeRelative:feedback_valencePositive 34.0000 0.738
## Pr(>|t|)
## (Intercept) 6.97e-07 ***
## ERSSuppression 0.296
## feedback_typeRelative 0.539
## feedback_valencePositive 0.771
## ERSSuppression:feedback_typeRelative 0.744
## ERSSuppression:feedback_valencePositive 0.310
## feedback_typeRelative:feedback_valencePositive 0.791
## ERSSuppression:feedback_typeRelative:feedback_valencePositive 0.466
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) ERSSpp fdbc_R fdbc_P ERSSp:_R ERSS:_P f_R:_P
## ERSSupprssn -0.378
## fdbck_typRl -0.707 0.267
## fdbck_vlncP -0.632 0.239 0.447
## ERSSpprs:_R 0.316 -0.837 -0.447 -0.200
## ERSSpprs:_P 0.309 -0.816 -0.218 -0.488 0.683
## fdbck_tR:_P 0.490 -0.185 -0.693 -0.775 0.310 0.378
## ERSSp:_R:_P -0.241 0.639 0.341 0.382 -0.763 -0.782 -0.493fixef(perf_model)## (Intercept)
## 4.9583333
## ERSSuppression
## 2.2916667
## feedback_typeRelative
## -0.7166667
## feedback_valencePositive
## 0.3791667
## ERSSuppression:feedback_typeRelative
## -0.8500000
## ERSSuppression:feedback_valencePositive
## -2.7291667
## feedback_typeRelative:feedback_valencePositive
## 0.4458333
## ERSSuppression:feedback_typeRelative:feedback_valencePositive
## 2.4958333ranef_perf <- ranef(perf_model)$ID
print(ranef_perf)## (Intercept)
## 1 -1.659028e+00
## 2 2.140681e+00
## 5 9.938875e-01
## 6 -3.153681e+00
## 7 1.551994e+00
## 8 -6.804307e-01
## 9 -2.163617e+00
## 10 1.972484e+00
## 12 -2.117745e+00
## 13 2.767594e+00
## 14 3.058115e-02
## 16 2.905210e-01
## 19 -4.052003e-01
## 21 4.441913e+00
## 22 3.497719e+00
## 23 -6.116231e-01
## 24 -3.058115e+00
## 26 -5.351702e-02
## 28 1.536703e+00
## 29 -1.299699e+00
## 33 -1.456427e+00
## 35 1.452605e+00
## 37 1.112389e+00
## 38 -1.551994e+00
## 39 -4.740079e-01
## 40 2.668206e+00
## 41 -2.752304e-01
## 42 1.016823e+00
## 45 -2.446492e-01
## 49 -1.987775e+00
## 52 -1.047405e+00
## 53 -1.697254e+00
## 55 -1.536703e+00
## 59 4.932722e-14In the presented linear mixed model, the dependent variable is performance (Perf), and it’s being predicted by emotion regulation suppression (ERS), feedback type (either relative or not), and feedback valence (either positive or not), as well as their interaction effects. The model was fitted using maximum likelihood estimation and t-tests were conducted using Satterthwaite’s method. The model includes a random intercept for each participant (ID), suggesting that there is substantial between-subject variability that the model accounts for. The standard deviation of the random intercepts is 1.9162, indicating substantial variation in the baseline performance between individuals. Looking at the fixed effects, the intercept term is significant (p < 0.001), meaning that when all predictors are zero, the estimated performance is significantly different from zero. ERS, feedback type, and feedback valence, and their interaction terms do not significantly predict performance individually. Their p-values are all above the typical significance level of 0.05, indicating that there is not enough evidence to conclude that these effects are different from zero in the population.
ggplot(long_data, aes(x = ERS, y = Perf, color = feedback_valence)) +
geom_point(alpha = 0.6, size = 3) +
facet_grid(rows = vars(feedback_type)) +
labs(
title = "Performance by ERS, separated by Feedback Type and Valence",
x = "ERS",
y = "Performance",
color = "Feedback Valence"
) +
theme_minimal() +
theme(
plot.title = element_text(face = "bold", hjust = 0.5, size = 14),
axis.title = element_text(face = "bold", size = 12),
legend.title = element_text(face = "bold", size = 10)
) +
scale_color_manual(values = c("Positive" = "blue", "Negative" = "red"))
In summary, the model suggests that there’s considerable variation in performance across individuals, but ERS, feedback type, and feedback valence, as well as their interaction effects, do not seem to predict performance significantly. Again the assumptions were tested.
resid <- residuals(perf_model)
fitted <- fitted(perf_model)
plot(fitted, resid, main = "Residuals vs Fitted", xlab = "Fitted values", ylab = "Residuals")
abline(h = 0, col = "red")
qqnorm(resid)
qqline(resid)
shapiro.test(resid)##
## Shapiro-Wilk normality test
##
## data: resid
## W = 0.98385, p-value = 0.5254boxplot(split(resid, long_data$feedback_type), main = "Residuals by feedback type", xlab = "Feedback type", ylab = "Residuals")
6. Conclusion
In light of the performed linear mixed models analysis on mood and performance, the hypotheses of this study haven’t received any support. The results revealed that the relationship between emotional regulation strategy (ERS), feedback type, and feedback valence was not statistically significant in predicting both mood and performance. In particular, among reappraisers, receiving negative feedback with relative standing did not conclusively lead to better performance and higher mood as opposed to receiving negative feedback with absolute standing. Likewise, suppressors receiving negative feedback with both relative and absolute standing did not markedly exhibit poorer performance or mood. These findings challenge the initial hypothesis and suggest that other variables might be playing a more critical role in determining one’s mood and performance.