Einlesen und Erstellen der Datensätze
MIDUS 3 Daten einlesen
agg = Data Set 1: Aggregate Data
dis = Data Set 2: Disposition Codes
cod = Data Set 3: Coded Text Data
load("~/Downloads/MIDUS 3/DS0001/36346-0001-Data.rda")
MIDUS3_agg <- da36346.0001
load("~/Downloads/MIDUS 3/DS0002/36346-0002-Data.rda")
MIDUS3_dis <- da36346.0002
load("~/Downloads/MIDUS 3/DS0003/36346-0003-Data.rda")
MIDUS3_cod <- da36346.0003
rm(da36346.0001)
rm(da36346.0002)
rm(da36346.0003)
Dimensionen der Datensätze anschauen
dim(MIDUS3_agg)
## [1] 3294 2613
dim(MIDUS3_cod)
## [1] 3137 183
dim(MIDUS3_dis)
## [1] 7108 6
Zusammenführen der drei einzelnen Datensätze
MIDUS3_gesamt <- merge(MIDUS3_agg, MIDUS3_cod, by = "M2ID")
MIDUS3_gesamt <- merge(MIDUS3_gesamt, MIDUS3_dis, by = "M2ID")
MIDUS 3 Biomarker Project Daten einlesen
bio_agg = Dataset 1: Biomarker Aggregate Dataset
bio_med = Dataset 2: Biomarker Medication Stacked Dataset
=>Eigentlich benötigen wir für die Fragestellung nur
MIDUS3_bio_agg
load("~/Downloads/MIDUS 3 Biomarker Project/DS0001/38837-0001-Data.rda")
MIDUS3_bio <- da38837.0001
load("~/Downloads/MIDUS 3 Biomarker Project/DS0002/38837-0002-Data.rda")
MIDUS3_bio_med<- da38837.0002
MIDUS3_bio_med <- MIDUS3_bio_med[!duplicated(MIDUS3_bio_med), ]
rm(da38837.0001)
rm(da38837.0002)
Datesätze mit den relevanten Variablen für die Fragestellung
erstellen
MIDUS3 <- MIDUS3_gesamt[,c('M2ID','C1PRAGE.x','B1PGENDER','C1SOPTIM','C1SPESSI','C1SORIEN','C1PDEPRE','C1PDEPAF','C1PB1')]
MIDUS3_bio <- MIDUS3_bio[,c('M2ID','C1PRAGE','C1PRSEX','C4QCESD','C4QCESDDA','C4QCESDPA','C4QCESDSC','C4QCESDI')]
Beide Datensätze zusammenführen
MIDUS <- merge(MIDUS3,MIDUS3_bio,by = 'M2ID')
any(is.na(MIDUS))
## [1] TRUE
sum(is.na(MIDUS))
## [1] 47
Bildung in eine numerische Zahl umwandeln
str(MIDUS$C1PB1)
## Factor w/ 12 levels "(01) NO SCHOOL/SOME GRADE SCHOOL (1-6)",..: 9 12 8 5 9 11 9 11 9 9 ...
MIDUS$C1PB1_num <- as.numeric(as.character(MIDUS$C1PB1))
## Warning: NAs introduced by coercion
unique(MIDUS$C1PB1)
## [1] (09) GRADUATED FROM A 4- OR 5-YEAR COLLEGE, OR BACHELOR'S DEG.
## [2] (12) PH.D., ED.D., MD, DDS, LLB, LLD, JD, OR OTHER PROFESS'NL DEG.
## [3] (08) GRAD. FROM 2-YEAR COLLEGE, VOCATIONAL SCHOOL, OR ASSOC. DEG.
## [4] (05) GRADUATED FROM HIGH SCHOOL
## [5] (11) MASTER'S DEGREE
## [6] (06) 1 TO 2 YEARS OF COLLEGE, NO DEGREE YET
## [7] (03) SOME HIGH SCHOOL (9-12 NO DIPLOMA/NO GED)
## [8] (07) 3 OR MORE YEARS OF COLLEGE, NO DEGREE YET
## [9] (04) GED
## [10] (10) SOME GRADUATE SCHOOL
## [11] (02) EIGHTH GRADE/JUNIOR HIGH SCHOOL (7-8)
## 12 Levels: (01) NO SCHOOL/SOME GRADE SCHOOL (1-6) ...
MIDUS$C1PB1_num <- NULL
Deskreptive Statistik des Datensatzes
library(psych)
library(knitr)
kable(describe(MIDUS), caption = "Deskriptive Statistiken", digits = 2)
Deskriptive Statistiken
| id |
1 |
622 |
14619.10 |
2704.84 |
14653.5 |
14627.76 |
3592.34 |
10019 |
19193 |
9174 |
-0.02 |
-1.25 |
108.45 |
| age |
2 |
622 |
61.00 |
9.74 |
60.0 |
60.63 |
10.38 |
43 |
90 |
47 |
0.35 |
-0.42 |
0.39 |
| gender* |
3 |
622 |
1.56 |
0.50 |
2.0 |
1.57 |
0.00 |
1 |
2 |
1 |
-0.24 |
-1.95 |
0.02 |
| optimism |
4 |
608 |
11.98 |
2.36 |
12.0 |
12.21 |
2.97 |
3 |
15 |
12 |
-0.87 |
0.66 |
0.10 |
| pessimism |
5 |
608 |
5.86 |
2.72 |
5.0 |
5.51 |
2.97 |
3 |
15 |
12 |
0.95 |
0.41 |
0.11 |
| lotr |
6 |
608 |
24.12 |
4.47 |
25.0 |
24.55 |
4.45 |
7 |
30 |
23 |
-0.89 |
0.58 |
0.18 |
| depression+anhedonia |
7 |
622 |
0.67 |
1.81 |
0.0 |
0.11 |
0.00 |
0 |
7 |
7 |
2.54 |
4.87 |
0.07 |
| depressedaffect |
8 |
622 |
0.53 |
1.68 |
0.0 |
0.00 |
0.00 |
0 |
7 |
7 |
3.00 |
7.48 |
0.07 |
| education_level* |
9 |
622 |
8.03 |
2.40 |
8.0 |
8.04 |
2.97 |
2 |
12 |
10 |
-0.10 |
-1.06 |
0.10 |
| education |
10 |
622 |
8.03 |
2.40 |
8.0 |
8.04 |
2.97 |
2 |
12 |
10 |
-0.10 |
-1.06 |
0.10 |
| age_bio |
11 |
622 |
61.00 |
9.74 |
60.0 |
60.63 |
10.38 |
43 |
90 |
47 |
0.35 |
-0.42 |
0.39 |
| sex* |
12 |
622 |
1.56 |
0.50 |
2.0 |
1.57 |
0.00 |
1 |
2 |
1 |
-0.24 |
-1.95 |
0.02 |
| cesd |
13 |
621 |
8.40 |
7.32 |
6.0 |
7.33 |
5.93 |
0 |
45 |
45 |
1.48 |
2.54 |
0.29 |
| cesdda |
14 |
621 |
1.75 |
2.74 |
1.0 |
1.15 |
1.48 |
0 |
17 |
17 |
2.32 |
6.22 |
0.11 |
| cesdpa |
15 |
621 |
9.38 |
2.69 |
10.0 |
9.77 |
2.97 |
0 |
12 |
12 |
-1.00 |
0.28 |
0.11 |
| cesdsc |
16 |
621 |
3.66 |
3.02 |
3.0 |
3.33 |
2.97 |
0 |
16 |
16 |
0.99 |
0.64 |
0.12 |
| cesdi |
17 |
621 |
0.36 |
0.77 |
0.0 |
0.17 |
0.00 |
0 |
5 |
5 |
2.46 |
6.70 |
0.03 |
kable(summary(MIDUS), caption = "Deskriptive Statistiken", digits = 2)
Deskriptive Statistiken
|
Min. :10019 |
Min. :43 |
(1) MALE :274 |
Min. : 3.00 |
Min. : 3.000 |
Min. : 7.00 |
Min. :0.0000 |
Min. :0.0000 |
(09) GRADUATED FROM A 4- OR 5-YEAR COLLEGE, OR
BACHELOR’S DEG. :147 |
Min. : 2.000 |
Min. :43 |
(1) MALE :274 |
Min. : 0.000 |
Min. : 0.000 |
Min. : 0.000 |
Min. : 0.000 |
Min. :0.0000 |
|
1st Qu.:12167 |
1st Qu.:54 |
(2) FEMALE:348 |
1st Qu.:11.00 |
1st Qu.: 3.000 |
1st Qu.:21.00 |
1st Qu.:0.0000 |
1st Qu.:0.0000 |
(11) MASTER’S DEGREE :108 |
1st Qu.: 6.000 |
1st Qu.:54 |
(2) FEMALE:348 |
1st Qu.: 3.000 |
1st Qu.: 0.000 |
1st Qu.: 8.000 |
1st Qu.: 1.000 |
1st Qu.:0.0000 |
|
Median :14654 |
Median :60 |
NA |
Median :12.00 |
Median : 5.000 |
Median :25.00 |
Median :0.0000 |
Median :0.0000 |
(05) GRADUATED FROM HIGH SCHOOL :103 |
Median : 8.000 |
Median :60 |
NA |
Median : 6.000 |
Median : 1.000 |
Median :10.000 |
Median : 3.000 |
Median :0.0000 |
|
Mean :14619 |
Mean :61 |
NA |
Mean :11.98 |
Mean : 5.863 |
Mean :24.12 |
Mean :0.6656 |
Mean :0.5322 |
(06) 1 TO 2 YEARS OF COLLEGE, NO DEGREE YET : 99 |
Mean : 8.027 |
Mean :61 |
NA |
Mean : 8.395 |
Mean : 1.749 |
Mean : 9.378 |
Mean : 3.662 |
Mean :0.3639 |
|
3rd Qu.:17040 |
3rd Qu.:67 |
NA |
3rd Qu.:14.00 |
3rd Qu.: 7.000 |
3rd Qu.:28.00 |
3rd Qu.:0.0000 |
3rd Qu.:0.0000 |
(08) GRAD. FROM 2-YEAR COLLEGE, VOCATIONAL SCHOOL, OR
ASSOC. DEG. : 70 |
3rd Qu.:10.000 |
3rd Qu.:67 |
NA |
3rd Qu.:12.000 |
3rd Qu.: 2.000 |
3rd Qu.:12.000 |
3rd Qu.: 5.000 |
3rd Qu.:0.0000 |
|
Max. :19193 |
Max. :90 |
NA |
Max. :15.00 |
Max. :15.000 |
Max. :30.00 |
Max. :7.0000 |
Max. :7.0000 |
(12) PH.D., ED.D., MD, DDS, LLB, LLD, JD, OR OTHER
PROFESS’NL DEG.: 34 |
Max. :12.000 |
Max. :90 |
NA |
Max. :45.000 |
Max. :17.000 |
Max. :12.000 |
Max. :16.000 |
Max. :5.0000 |
|
NA |
NA |
NA |
NA’s :14 |
NA’s :14 |
NA’s :14 |
NA |
NA |
(Other) : 61 |
NA |
NA |
NA |
NA’s :1 |
NA’s :1 |
NA’s :1 |
NA’s :1 |
NA’s :1 |
cor(MIDUS[, c("age", "optimism", "pessimism","depressedaffect","education","cesd")], method = "pearson", use = "pairwise.complete.obs")
## age optimism pessimism depressedaffect education
## age 1.00000000 0.15008883 -0.1558680 -0.12729081 -0.04765306
## optimism 0.15008883 1.00000000 -0.5463875 -0.17337870 0.05802677
## pessimism -0.15586799 -0.54638752 1.0000000 0.25112815 -0.20982539
## depressedaffect -0.12729081 -0.17337870 0.2511282 1.00000000 -0.02201579
## education -0.04765306 0.05802677 -0.2098254 -0.02201579 1.00000000
## cesd -0.10080345 -0.35679774 0.3730952 0.34613199 -0.10960558
## cesd
## age -0.1008035
## optimism -0.3567977
## pessimism 0.3730952
## depressedaffect 0.3461320
## education -0.1096056
## cesd 1.0000000
corr.test(MIDUS[, c("age", "optimism", "pessimism","depressedaffect","education","cesd")], method = "pearson", use = "pairwise.complete.obs")
## Call:corr.test(x = MIDUS[, c("age", "optimism", "pessimism", "depressedaffect",
## "education", "cesd")], use = "pairwise.complete.obs", method = "pearson")
## Correlation matrix
## age optimism pessimism depressedaffect education cesd
## age 1.00 0.15 -0.16 -0.13 -0.05 -0.10
## optimism 0.15 1.00 -0.55 -0.17 0.06 -0.36
## pessimism -0.16 -0.55 1.00 0.25 -0.21 0.37
## depressedaffect -0.13 -0.17 0.25 1.00 -0.02 0.35
## education -0.05 0.06 -0.21 -0.02 1.00 -0.11
## cesd -0.10 -0.36 0.37 0.35 -0.11 1.00
## Sample Size
## age optimism pessimism depressedaffect education cesd
## age 622 608 608 622 622 621
## optimism 608 608 608 608 608 607
## pessimism 608 608 608 608 608 607
## depressedaffect 622 608 608 622 622 621
## education 622 608 608 622 622 621
## cesd 621 607 607 621 621 621
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## age optimism pessimism depressedaffect education cesd
## age 0.00 0.00 0 0.01 0.47 0.05
## optimism 0.00 0.00 0 0.00 0.46 0.00
## pessimism 0.00 0.00 0 0.00 0.00 0.00
## depressedaffect 0.00 0.00 0 0.00 0.58 0.00
## education 0.24 0.15 0 0.58 0.00 0.03
## cesd 0.01 0.00 0 0.00 0.01 0.00
##
## To see confidence intervals of the correlations, print with the short=FALSE option
Hypothese 1 prüfen
cor_result_opt_dep <- cor.test(MIDUS$optimism, MIDUS$cesd, method = "pearson")
cor_result_opt_dep
##
## Pearson's product-moment correlation
##
## data: MIDUS$optimism and MIDUS$cesd
## t = -9.3944, df = 605, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4243303 -0.2853180
## sample estimates:
## cor
## -0.3567977
Effektstärke (r) und 95%-Konfidenzintervall ausgeben
r_value_opt_dep <- cor_result_opt_dep$estimate
ci_lower_opt_dep <- cor_result_opt_dep$conf.int[1]
ci_upper_opt_dep <- cor_result_opt_dep$conf.int[2]
cat("Korrelationskoeffizient r =", round(r_value_opt_dep, 2), "\n")
## Korrelationskoeffizient r = -0.36
cat("95%-Konfidenzintervall: [", round(ci_lower_opt_dep, 2), ",", round(ci_upper_opt_dep, 3), "]\n")
## 95%-Konfidenzintervall: [ -0.42 , -0.285 ]
=>Die erste Hypothese ist mit einem p-Wert < 2.2e-16
signifikant
=>Die Korrelation von Optimismus und Depression liegt bei
-0,36
Aus Interesse anschauen, wie Optimismus mit Bildung korreliert
ist
cor_result_opt_edu <- cor.test(MIDUS$optimism, MIDUS$education, method = "pearson")
cor_result_opt_edu
##
## Pearson's product-moment correlation
##
## data: MIDUS$optimism and MIDUS$education
## t = 1.4309, df = 606, p-value = 0.153
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.02158848 0.13691070
## sample estimates:
## cor
## 0.05802677
cor_result_opt_pes <- cor.test(MIDUS$optimism, MIDUS$pessimism, method = "pearson")
cor_result_opt_pes
##
## Pearson's product-moment correlation
##
## data: MIDUS$optimism and MIDUS$pessimism
## t = -16.06, df = 606, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5998422 -0.4880770
## sample estimates:
## cor
## -0.5463875
Effektstärke (r) und 95%-Konfidenzintervall für die ausgeben
r_value_opt_edu <- cor_result_opt_edu$estimate
ci_lower_opt_edu <- cor_result_opt_edu$conf.int[1]
ci_upper_opt_edu <- cor_result_opt_edu$conf.int[2]
cat("Korrelationskoeffizient r =", round(r_value_opt_edu, 2), "\n")
## Korrelationskoeffizient r = 0.06
cat("95%-Konfidenzintervall: [", round(ci_lower_opt_edu, 2), ",", round(ci_upper_opt_edu, 3), "]\n")
## 95%-Konfidenzintervall: [ -0.02 , 0.137 ]
=>Korrelation von Optimismus und Bildung nicht signifikant
Aus Interesse anschauen, wie Depression mit Bildung korreliert
ist
cor_result_dep_edu <- cor.test(MIDUS$education, MIDUS$cesd, method = "pearson")
cor_result_dep_edu
##
## Pearson's product-moment correlation
##
## data: MIDUS$education and MIDUS$cesd
## t = -2.7435, df = 619, p-value = 0.006255
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.18667414 -0.03119624
## sample estimates:
## cor
## -0.1096056
Effektstärke (r) und 95%-Konfidenzintervall für die ausgeben
r_value_dep_edu <- cor_result_dep_edu$estimate
ci_lower_dep_edu <- cor_result_dep_edu$conf.int[1]
ci_upper_dep_edu <- cor_result_dep_edu$conf.int[2]
cat("Korrelationskoeffizient r =", round(r_value_dep_edu, 2), "\n")
## Korrelationskoeffizient r = -0.11
cat("95%-Konfidenzintervall: [", round(ci_lower_dep_edu, 2), ",", round(ci_upper_dep_edu, 3), "]\n")
## 95%-Konfidenzintervall: [ -0.19 , -0.031 ]
=>Korrelation von Depression und Bildung ist signifikant und
liegt bei ca. -0.11
Aus Interesse anschauen, wie Alter mit Optimismus korreliert
ist
cor_result_opt_age <- cor.test(MIDUS$optimism, MIDUS$age, method = "pearson")
cor_result_opt_age
##
## Pearson's product-moment correlation
##
## data: MIDUS$optimism and MIDUS$age
## t = 3.7371, df = 606, p-value = 0.0002038
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.07142561 0.22689659
## sample estimates:
## cor
## 0.1500888
Aus Interesse anschauen, wie Alter mit Bildung korreliert ist
cor_result_edu_age <- cor.test(MIDUS$education, MIDUS$age, method = "pearson")
cor_result_edu_age
##
## Pearson's product-moment correlation
##
## data: MIDUS$education and MIDUS$age
## t = -1.1879, df = 620, p-value = 0.2353
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.12579684 0.03107841
## sample estimates:
## cor
## -0.04765306
Neues Package installieren, um später den Johnson-Neyman-Test
durchführen zu können und Plots abzubilden
library(interactions)
library(effectsize)
##
## Attaching package: 'effectsize'
## The following object is masked from 'package:psych':
##
## phi
library(apaTables)
Hypothese 2 prüfen
Variable zentrieren, Zentrierung ohne Standardisierung
MIDUS$optimism_z <- scale(MIDUS$optimism, scale = FALSE)
MIDUS$education_z <- scale(MIDUS$education, scale = FALSE)
Hierarchische Regression
Modell 1: Hauptmodell ohne Interaktion
modell1 <- lm(cesd ~ optimism_z + education_z, data = MIDUS)
summary(modell1)
##
## Call:
## lm(formula = cesd ~ optimism_z + education_z, data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.699 -4.614 -1.595 3.077 35.749
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.4363 0.2788 30.259 <2e-16 ***
## optimism_z -1.1031 0.1187 -9.296 <2e-16 ***
## education_z -0.2765 0.1178 -2.346 0.0193 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.869 on 604 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.1352, Adjusted R-squared: 0.1323
## F-statistic: 47.21 on 2 and 604 DF, p-value: < 2.2e-16
standardize_parameters(modell1)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## -----------------------------------------
## (Intercept) | -3.14e-16 | [-0.07, 0.07]
## optimism z | -0.35 | [-0.43, -0.28]
## education z | -0.09 | [-0.16, -0.01]
library(broom)
tidy_mod1 <- broom::tidy(modell1)
kable(tidy_mod1, caption = "Regressionsoutput Modell 1")
Regressionsoutput Modell 1
| (Intercept) |
8.4362595 |
0.2787976 |
30.259444 |
0.0000000 |
| optimism_z |
-1.1031373 |
0.1186637 |
-9.296336 |
0.0000000 |
| education_z |
-0.2764515 |
0.1178313 |
-2.346164 |
0.0192901 |
library(gtsummary)
modell1 %>% tbl_regression()
| Characteristic |
Beta |
95% CI |
p-value |
| optimism_z |
-1.1 |
-1.3, -0.87 |
<0.001 |
| education_z |
-0.28 |
-0.51, -0.05 |
0.019 |
| Abbreviation: CI = Confidence Interval |
95%-Konfidenzintervall berechnen
confint(modell1)
## 2.5 % 97.5 %
## (Intercept) 7.8887291 8.98378986
## optimism_z -1.3361808 -0.87009379
## education_z -0.5078602 -0.04504274
Effektsärke berechnen
library(effectsize)
standardize_parameters(modell1)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## -----------------------------------------
## (Intercept) | -3.14e-16 | [-0.07, 0.07]
## optimism z | -0.35 | [-0.43, -0.28]
## education z | -0.09 | [-0.16, -0.01]
summary(modell1)$r.squared
## [1] 0.135186
summary(modell1)$adj.r.squared
## [1] 0.1323224
ANOVA berechnen
modell1.1 <- anova(modell1)
kable(modell1.1, caption = "ANOVA-Tabelle Modell 1")
ANOVA-Tabelle Modell 1
| optimism_z |
1 |
4194.7955 |
4194.7955 |
88.911600 |
0.0000000 |
| education_z |
1 |
259.6983 |
259.6983 |
5.504486 |
0.0192901 |
| Residuals |
604 |
28496.3548 |
47.1794 |
NA |
NA |
Modell 2: Modell mit Interaktion
modell2 <- lm(cesd ~ optimism_z * education_z, data = MIDUS)
summary(modell2)
##
## Call:
## lm(formula = cesd ~ optimism_z * education_z, data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.213 -4.617 -1.553 3.059 35.801
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.42469 0.27922 30.172 <2e-16 ***
## optimism_z -1.09807 0.11885 -9.239 <2e-16 ***
## education_z -0.27302 0.11793 -2.315 0.0209 *
## optimism_z:education_z 0.04014 0.04843 0.829 0.4076
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.871 on 603 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.1362, Adjusted R-squared: 0.1319
## F-statistic: 31.68 on 3 and 603 DF, p-value: < 2.2e-16
standardize_parameters(modell2)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## ------------------------------------------------------
## (Intercept) | -1.56e-03 | [-0.08, 0.07]
## optimism z | -0.35 | [-0.43, -0.28]
## education z | -0.09 | [-0.16, -0.01]
## optimism z × education z | 0.03 | [-0.04, 0.10]
tidy_mod2 <- broom::tidy(modell2)
kable(tidy_mod2, caption = "Regressionsoutput Modell 2")
Regressionsoutput Modell 2
| (Intercept) |
8.4246905 |
0.2792190 |
30.1723372 |
0.0000000 |
| optimism_z |
-1.0980709 |
0.1188518 |
-9.2389967 |
0.0000000 |
| education_z |
-0.2730171 |
0.1179346 |
-2.3149864 |
0.0209485 |
| optimism_z:education_z |
0.0401365 |
0.0484288 |
0.8287734 |
0.4075606 |
95%-Konfidenzintervall berechnen
confint(modell1)
## 2.5 % 97.5 %
## (Intercept) 7.8887291 8.98378986
## optimism_z -1.3361808 -0.87009379
## education_z -0.5078602 -0.04504274
Effektsärke berechnen
library(effectsize)
standardize_parameters(modell2)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## ------------------------------------------------------
## (Intercept) | -1.56e-03 | [-0.08, 0.07]
## optimism z | -0.35 | [-0.43, -0.28]
## education z | -0.09 | [-0.16, -0.01]
## optimism z × education z | 0.03 | [-0.04, 0.10]
summary(modell2)$r.squared
## [1] 0.13617
summary(modell2)$adj.r.squared
## [1] 0.1318723
ANOVA berechnen
modell2.1 <- anova(modell2)
kable(modell2.1, caption = "ANOVA-Tabelle Modell 2")
ANOVA-Tabelle Modell 2
| optimism_z |
1 |
4194.7955 |
4194.79551 |
88.8655047 |
0.0000000 |
| education_z |
1 |
259.6983 |
259.69833 |
5.5016324 |
0.0193218 |
| optimism_z:education_z |
1 |
32.4227 |
32.42270 |
0.6868653 |
0.4075606 |
| Residuals |
603 |
28463.9321 |
47.20387 |
NA |
NA |
Interaktionsplot für Modell 2
interact_plot(modell2, pred = "optimism_z", modx = "education_z")
Testen, ob das Modell mit Interaktion signifikant besser passt
modell_ges <- anova(modell1,modell2)
kable(modell_ges, caption = "ANOVA-Tabelle")
ANOVA-Tabelle
| 604 |
28496.35 |
NA |
NA |
NA |
NA |
| 603 |
28463.93 |
1 |
32.4227 |
0.6868653 |
0.4075606 |
r2_diff <- summary(modell2)$r.squared - summary(modell1)$r.squared
cat("R²-Zuwachs durch Interaktion:", round(r2_diff, 4))
## R²-Zuwachs durch Interaktion: 0.001
=>Hypothese 2 kann nicht bestätigt werden, da das Modell mit
Interaktion nicht signifikant besser passt.
Johnson Neyman Test durchführen
johnson_neyman(modell2, pred = "optimism_z", modx = "education_z")
## JOHNSON-NEYMAN INTERVAL
##
## When education_z is INSIDE the interval [-19.93, 7.77], the slope of
## optimism_z is p < .05.
##
## Note: The range of observed values of education_z is [-6.03, 3.97]
=>Optimismus wirkt über alle Bildungslevel hinweg signifikant –
ohne wesentliche Veränderung je nach Bildung, also ist es nicht sinnvoll
die Interaktion in das Regressionmodell aufzunehmen, da sie keine
zusätzliche Varianzaufklärung bietet
Für depressive Symptome zum Zeitpunkt der Erhebung des Optimismus
kontrollieren
modell1_kon <- lm(cesd ~ optimism_z + education_z + depressedaffect, data = MIDUS)
summary(modell1_kon)
##
## Call:
## lm(formula = cesd ~ optimism_z + education_z + depressedaffect,
## data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.052 -4.393 -1.479 2.831 30.137
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.7513 0.2773 27.953 < 2e-16 ***
## optimism_z -0.9395 0.1143 -8.217 1.28e-15 ***
## education_z -0.2627 0.1118 -2.349 0.0191 *
## depressedaffect 1.3387 0.1625 8.238 1.09e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.517 on 603 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.2227, Adjusted R-squared: 0.2188
## F-statistic: 57.58 on 3 and 603 DF, p-value: < 2.2e-16
standardize_parameters(modell1_kon)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## ---------------------------------------------
## (Intercept) | -3.47e-16 | [-0.07, 0.07]
## optimism z | -0.30 | [-0.37, -0.23]
## education z | -0.08 | [-0.16, -0.01]
## depressedaffect | 0.30 | [ 0.23, 0.37]
tidy_mod1_kon <- broom::tidy(modell1_kon)
kable(tidy_mod1_kon, caption = "Regressionsoutput Modell 1 (kontrolliert für Depressivität T1)")
Regressionsoutput Modell 1 (kontrolliert für Depressivität
T1)
| (Intercept) |
7.7513382 |
0.2772946 |
27.953438 |
0.0000000 |
| optimism_z |
-0.9395024 |
0.1143330 |
-8.217249 |
0.0000000 |
| education_z |
-0.2626933 |
0.1118171 |
-2.349314 |
0.0191297 |
| depressedaffect |
1.3386893 |
0.1624947 |
8.238357 |
0.0000000 |
modell1.1_kon <- anova(modell1_kon)
kable(modell1.1_kon, caption = "ANOVA-Tabelle Modell 1 (kontrolliert für Depressivität T1)")
ANOVA-Tabelle Modell 1 (kontrolliert für Depressivität
T1)
| optimism_z |
1 |
4194.7955 |
4194.79551 |
98.755250 |
0.000000 |
| education_z |
1 |
259.6983 |
259.69833 |
6.113903 |
0.013687 |
| depressedaffect |
1 |
2882.9147 |
2882.91470 |
67.870523 |
0.000000 |
| Residuals |
603 |
25613.4401 |
42.47668 |
NA |
NA |
modell2_kon <- lm(cesd ~ optimism_z * education_z + depressedaffect, data = MIDUS)
summary(modell2_kon)
##
## Call:
## lm(formula = cesd ~ optimism_z * education_z + depressedaffect,
## data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.052 -4.306 -1.298 2.930 30.142
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.73642 0.27768 27.861 < 2e-16 ***
## optimism_z -0.93326 0.11449 -8.151 2.10e-15 ***
## education_z -0.25867 0.11188 -2.312 0.0211 *
## depressedaffect 1.34154 0.16251 8.255 9.64e-16 ***
## optimism_z:education_z 0.04668 0.04595 1.016 0.3100
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.517 on 602 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.224, Adjusted R-squared: 0.2189
## F-statistic: 43.45 on 4 and 602 DF, p-value: < 2.2e-16
standardize_parameters(modell2_kon)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## ------------------------------------------------------
## (Intercept) | -1.81e-03 | [-0.07, 0.07]
## optimism z | -0.30 | [-0.37, -0.23]
## education z | -0.08 | [-0.15, -0.01]
## depressedaffect | 0.30 | [ 0.23, 0.37]
## optimism z × education z | 0.04 | [-0.03, 0.10]
tidy_mod2_kon <- broom::tidy(modell2_kon)
kable(tidy_mod2_kon, caption = "Regressionsoutput Modell 2 (kontrolliert für Depressivität T1)")
Regressionsoutput Modell 2 (kontrolliert für Depressivität
T1)
| (Intercept) |
7.7364236 |
0.2776754 |
27.861391 |
0.0000000 |
| optimism_z |
-0.9332612 |
0.1144948 |
-8.151125 |
0.0000000 |
| education_z |
-0.2586694 |
0.1118842 |
-2.311939 |
0.0211176 |
| depressedaffect |
1.3415398 |
0.1625146 |
8.254891 |
0.0000000 |
| optimism_z:education_z |
0.0466838 |
0.0459455 |
1.016069 |
0.3100048 |
modell2.1_kon <- anova(modell2_kon)
kable(modell2.1_kon, caption = "ANOVA-Tabelle Modell 2 (kontrolliert für Depressivität T1)")
ANOVA-Tabelle Modell 2 (kontrolliert für Depressivität
T1)
| optimism_z |
1 |
4194.7955 |
4194.7955 |
98.760556 |
0.0000000 |
| education_z |
1 |
259.6983 |
259.6983 |
6.114232 |
0.0136849 |
| depressedaffect |
1 |
2882.9147 |
2882.9147 |
67.874169 |
0.0000000 |
| optimism_z:education_z |
1 |
43.8504 |
43.8504 |
1.032396 |
0.3100048 |
| Residuals |
602 |
25569.5897 |
42.4744 |
NA |
NA |
Testen ob das Modell mit Interaktion signifikant besser passt
modell_ges_kon <- anova(modell1_kon,modell2_kon)
kable(modell_ges_kon, caption = "ANOVA-Tabelle (kontrolliert für Depressivität T1)")
ANOVA-Tabelle (kontrolliert für Depressivität T1)
| 603 |
25613.44 |
NA |
NA |
NA |
NA |
| 602 |
25569.59 |
1 |
43.8504 |
1.032396 |
0.3100048 |
r2_diff_kon <- summary(modell2_kon)$r.squared - summary(modell1_kon)$r.squared
cat("R²-Zuwachs durch Interaktion:", round(r2_diff_kon, 4))
## R²-Zuwachs durch Interaktion: 0.0013
=>Auch wenn für depressive Symptome zum Zeitpunkt T1 kontrolliert
wird, ist der Effekt der Interaktion von SES und Optimismus nicht
signifikant
Hypothese 2a überprüfen
library(interactions)
slopes <- sim_slopes(modell2, pred = "optimism_z", modx = "education_z")
slopes.table <- slopes$slopes
print(slopes.table)
## Value of education_z Est. S.E. 2.5% 97.5% t val.
## 1 -2.35890961 -1.192749 0.1605603 -1.508074 -0.8774240 -7.428670
## 2 0.01220753 -1.097581 0.1188836 -1.331057 -0.8641047 -9.232398
## 3 2.38332466 -1.002413 0.1698794 -1.336040 -0.6687856 -5.900732
## p
## 1 3.767659e-13
## 2 4.444688e-19
## 3 6.037482e-09
slopes_df <- as.data.frame(slopes$slopes)
slopes_df
## Value of education_z Est. S.E. 2.5% 97.5% t val.
## 1 -2.35890961 -1.192749 0.1605603 -1.508074 -0.8774240 -7.428670
## 2 0.01220753 -1.097581 0.1188836 -1.331057 -0.8641047 -9.232398
## 3 2.38332466 -1.002413 0.1698794 -1.336040 -0.6687856 -5.900732
## p
## 1 3.767659e-13
## 2 4.444688e-19
## 3 6.037482e-09
Alle Effekte sind signifikant negativ → mehr Optimismus = weniger
depressive Symptome – für alle SES-Niveaus.
->Aber: Der Effekt wird schwächer, je höher der SES (von -1.19 →
-1.10 → -1.00).
->Der Effekt von Optimismus auf Depression ist bei niedriger
Bildung stärker, nicht bei hoher.
=>Somit ist auch Hypothese 2a nicht signifikant, allerdings zeigt
sich ein gegenteiliger Effekt, nämlich, dass Optimismus bei niedrigem
SES stärker wirkt.
Hypothese 3 prüfen
Variable zentrieren, Zentrierung ohne Standardisierung
MIDUS$age_z <- scale(MIDUS$age, scale = FALSE)
Hierarchische Regression
Modell 1: Hauptmodell ohne Interaktion
modell1_age <- lm(cesd ~ optimism_z + age_z, data = MIDUS)
summary(modell1_age)
##
## Call:
## lm(formula = cesd ~ optimism_z + age_z, data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.608 -4.647 -1.482 3.288 34.944
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.43546 0.27965 30.164 <2e-16 ***
## optimism_z -1.09199 0.12037 -9.072 <2e-16 ***
## age_z -0.03918 0.02916 -1.343 0.18
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.89 on 604 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.1299, Adjusted R-squared: 0.127
## F-statistic: 45.09 on 2 and 604 DF, p-value: < 2.2e-16
standardize_parameters(modell1_age)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## -----------------------------------------
## (Intercept) | -3.25e-16 | [-0.07, 0.07]
## optimism z | -0.35 | [-0.42, -0.27]
## age z | -0.05 | [-0.13, 0.02]
tidy_mod1_age <- broom::tidy(modell1_age)
kable(tidy_mod1_age, caption = "Regressionsoutput Modell 1")
Regressionsoutput Modell 1
| (Intercept) |
8.4354580 |
0.2796502 |
30.164323 |
0.0000000 |
| optimism_z |
-1.0919895 |
0.1203682 |
-9.072077 |
0.0000000 |
| age_z |
-0.0391805 |
0.0291645 |
-1.343435 |
0.1796358 |
95%-Konfidenzintervall berechnen
confint(modell1_age)
## 2.5 % 97.5 %
## (Intercept) 7.88625326 8.98466280
## optimism_z -1.32838054 -0.85559851
## age_z -0.09645659 0.01809552
Effektsärke berechnen
library(effectsize)
standardize_parameters(modell1_age)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## -----------------------------------------
## (Intercept) | -3.25e-16 | [-0.07, 0.07]
## optimism z | -0.35 | [-0.42, -0.27]
## age z | -0.05 | [-0.13, 0.02]
summary(modell1_age)$r.squared
## [1] 0.1299046
summary(modell1_age)$adj.r.squared
## [1] 0.1270235
ANOVA berechnen
modell1.1_age <- anova(modell1_age)
kable(modell1.1_age, caption = "ANOVA-Tabelle Modell 1")
ANOVA-Tabelle Modell 1
| optimism_z |
1 |
4194.79551 |
4194.79551 |
88.371909 |
0.0000000 |
| age_z |
1 |
85.67015 |
85.67015 |
1.804816 |
0.1796358 |
| Residuals |
604 |
28670.38301 |
47.46752 |
NA |
NA |
Modell 2: Modell mit Interaktion
modell2_age <- lm(cesd ~ optimism_z * age_z, data = MIDUS)
summary(modell2_age)
##
## Call:
## lm(formula = cesd ~ optimism_z * age_z, data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.149 -4.796 -1.414 3.219 34.878
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.413759 0.283481 29.680 <2e-16 ***
## optimism_z -1.086662 0.120959 -8.984 <2e-16 ***
## age_z -0.039845 0.029216 -1.364 0.173
## optimism_z:age_z 0.006038 0.012623 0.478 0.633
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.894 on 603 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.1302, Adjusted R-squared: 0.1259
## F-statistic: 30.1 on 3 and 603 DF, p-value: < 2.2e-16
standardize_parameters(modell2_age)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## ------------------------------------------------
## (Intercept) | -2.94e-03 | [-0.08, 0.07]
## optimism z | -0.35 | [-0.42, -0.27]
## age z | -0.05 | [-0.13, 0.02]
## optimism z × age z | 0.02 | [-0.06, 0.10]
tidy_mod2_age <- broom::tidy(modell2_age)
kable(tidy_mod2_age, caption = "Regressionsoutput Modell 2")
Regressionsoutput Modell 2
| (Intercept) |
8.4137595 |
0.2834813 |
29.6801217 |
0.0000000 |
| optimism_z |
-1.0866623 |
0.1209588 |
-8.9837365 |
0.0000000 |
| age_z |
-0.0398453 |
0.0292162 |
-1.3638091 |
0.1731365 |
| optimism_z:age_z |
0.0060383 |
0.0126226 |
0.4783721 |
0.6325588 |
95%-Konfidenzintervall berechnen
confint(modell2_age)
## 2.5 % 97.5 %
## (Intercept) 7.85702887 8.97049004
## optimism_z -1.32421403 -0.84911051
## age_z -0.09722303 0.01753252
## optimism_z:age_z -0.01875136 0.03082801
Effektsärke berechnen
library(effectsize)
standardize_parameters(modell2_age)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## ------------------------------------------------
## (Intercept) | -2.94e-03 | [-0.08, 0.07]
## optimism z | -0.35 | [-0.42, -0.27]
## age z | -0.05 | [-0.13, 0.02]
## optimism z × age z | 0.02 | [-0.06, 0.10]
summary(modell2_age)$r.squared
## [1] 0.1302346
summary(modell2_age)$adj.r.squared
## [1] 0.1259075
ANOVA berechnen
modell2.1_age <- anova(modell2_age)
kable(modell2.1_age, caption = "ANOVA-Tabelle Modell 2")
ANOVA-Tabelle Modell 2
| optimism_z |
1 |
4194.79551 |
4194.79551 |
88.2590801 |
0.0000000 |
| age_z |
1 |
85.67015 |
85.67015 |
1.8025119 |
0.1799143 |
| optimism_z:age_z |
1 |
10.87635 |
10.87635 |
0.2288399 |
0.6325588 |
| Residuals |
603 |
28659.50667 |
47.52820 |
NA |
NA |
Interaktionsplot für Modell 2
interact_plot(modell2_age, pred = "optimism_z", modx = "age_z")
### Testen, ob das Modell mit Interaktion signifikant besser passt
modell_ges_age <- anova(modell1_age,modell2_age)
kable(modell_ges_age, caption = "ANOVA-Tabelle")
ANOVA-Tabelle
| 604 |
28670.38 |
NA |
NA |
NA |
NA |
| 603 |
28659.51 |
1 |
10.87635 |
0.2288399 |
0.6325588 |
r2_diff_age <- summary(modell2_age)$r.squared - summary(modell1_age)$r.squared
cat("R²-Zuwachs durch Interaktion:", round(r2_diff_age, 4))
## R²-Zuwachs durch Interaktion: 3e-04
Hypothese 3 nicht bestätigt, da die Interaktion mit Alter nicht
signifikant zusätzliche Varianz aufklärt
Für depressive Symptome zum Zeitpunkt der Erhebung des Optimismus
kontrollieren
modell1_age_kon <- lm(cesd ~ optimism_z + age_z + depressedaffect, data = MIDUS)
summary(modell1_age_kon)
##
## Call:
## lm(formula = cesd ~ optimism_z + age_z + depressedaffect, data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.133 -4.602 -1.313 3.025 29.928
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.75125 0.27866 27.816 < 2e-16 ***
## optimism_z -0.94317 0.11581 -8.144 2.20e-15 ***
## age_z -0.01603 0.02785 -0.575 0.565
## depressedaffect 1.33475 0.16403 8.137 2.32e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.545 on 603 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.216, Adjusted R-squared: 0.2121
## F-statistic: 55.38 on 3 and 603 DF, p-value: < 2.2e-16
standardize_parameters(modell1_age_kon)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## ---------------------------------------------
## (Intercept) | -3.55e-16 | [-0.07, 0.07]
## optimism z | -0.30 | [-0.37, -0.23]
## age z | -0.02 | [-0.09, 0.05]
## depressedaffect | 0.30 | [ 0.23, 0.37]
tidy_mod1_age_kon <- broom::tidy(modell1_age_kon)
kable(tidy_mod1_age_kon, caption = "Regressionsoutput Modell 1 (kontrolliert für Depressivität T1)")
Regressionsoutput Modell 1 (kontrolliert für Depressivität
T1)
| (Intercept) |
7.7512507 |
0.2786641 |
27.8157520 |
0.0000000 |
| optimism_z |
-0.9431651 |
0.1158065 |
-8.1443192 |
0.0000000 |
| age_z |
-0.0160271 |
0.0278528 |
-0.5754226 |
0.5652202 |
| depressedaffect |
1.3347483 |
0.1640319 |
8.1371284 |
0.0000000 |
modell1.1_age_kon <- anova(modell1_age_kon)
kable(modell1.1_age_kon, caption = "ANOVA-Tabelle Modell 1 (kontrolliert für Depressivität T1)")
ANOVA-Tabelle Modell 1 (kontrolliert für Depressivität
T1)
| optimism_z |
1 |
4194.79551 |
4194.79551 |
97.913275 |
0.0000000 |
| age_z |
1 |
85.67015 |
85.67015 |
1.999679 |
0.1578486 |
| depressedaffect |
1 |
2836.68788 |
2836.68788 |
66.212858 |
0.0000000 |
| Residuals |
603 |
25833.69513 |
42.84195 |
NA |
NA |
modell2_age_kon <- lm(cesd ~ optimism_z * age_z + depressedaffect, data = MIDUS)
summary(modell2_age_kon)
##
## Call:
## lm(formula = cesd ~ optimism_z * age_z + depressedaffect, data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.180 -4.618 -1.210 2.994 30.177
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.718447 0.282441 27.328 < 2e-16 ***
## optimism_z -0.935157 0.116380 -8.035 4.94e-15 ***
## age_z -0.016926 0.027892 -0.607 0.544
## depressedaffect 1.337947 0.164156 8.150 2.11e-15 ***
## optimism_z:age_z 0.008672 0.011993 0.723 0.470
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.548 on 602 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.2167, Adjusted R-squared: 0.2115
## F-statistic: 41.63 on 4 and 602 DF, p-value: < 2.2e-16
standardize_parameters(modell2_age_kon)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## ------------------------------------------------
## (Intercept) | -4.23e-03 | [-0.08, 0.07]
## optimism z | -0.30 | [-0.37, -0.23]
## age z | -0.02 | [-0.09, 0.05]
## depressedaffect | 0.30 | [ 0.23, 0.37]
## optimism z × age z | 0.03 | [-0.05, 0.10]
tidy_mod2_age_kon <- broom::tidy(modell2_age_kon)
kable(tidy_mod2_age_kon, caption = "Regressionsoutput Modell 2 (kontrolliert für Depressivität T1)")
Regressionsoutput Modell 2 (kontrolliert für Depressivität
T1)
| (Intercept) |
7.7184469 |
0.2824414 |
27.3276023 |
0.0000000 |
| optimism_z |
-0.9351574 |
0.1163804 |
-8.0353489 |
0.0000000 |
| age_z |
-0.0169263 |
0.0278915 |
-0.6068624 |
0.5441711 |
| depressedaffect |
1.3379470 |
0.1641564 |
8.1504401 |
0.0000000 |
| optimism_z:age_z |
0.0086724 |
0.0119933 |
0.7231027 |
0.4698976 |
modell2.1_age_kon <- anova(modell2_age_kon)
kable(modell2.1_age_kon, caption = "ANOVA-Tabelle Modell 2 (kontrolliert für Depressivität T1)")
ANOVA-Tabelle Modell 2 (kontrolliert für Depressivität
T1)
| optimism_z |
1 |
4194.79551 |
4194.79551 |
97.8358013 |
0.0000000 |
| age_z |
1 |
85.67015 |
85.67015 |
1.9980969 |
0.1580137 |
| depressedaffect |
1 |
2836.68788 |
2836.68788 |
66.1604675 |
0.0000000 |
| optimism_z:age_z |
1 |
22.41883 |
22.41883 |
0.5228776 |
0.4698976 |
| Residuals |
602 |
25811.27629 |
42.87587 |
NA |
NA |
Testen ob das Modell mit Interaktion signifikant besser passt
modell_age_ges_kon <- anova(modell1_age_kon,modell2_age_kon)
kable(modell_age_ges_kon, caption = "ANOVA-Tabelle (kontrolliert für Depressivität T1)")
ANOVA-Tabelle (kontrolliert für Depressivität T1)
| 603 |
25833.70 |
NA |
NA |
NA |
NA |
| 602 |
25811.28 |
1 |
22.41883 |
0.5228776 |
0.4698976 |
r2_age_diff_kon <- summary(modell2_age_kon)$r.squared - summary(modell1_age_kon)$r.squared
cat("R²-Zuwachs durch Interaktion:", round(r2_age_diff_kon, 4))
## R²-Zuwachs durch Interaktion: 7e-04
Johnson Neyman Test durchführen
johnson_neyman(modell2_age, pred = "optimism_z", modx = "age_z")
## JOHNSON-NEYMAN INTERVAL
##
## When age_z is INSIDE the interval [-58.07, 33.49], the slope of optimism_z
## is p < .05.
##
## Note: The range of observed values of age_z is [-18.00, 29.00]
#### =>Der Zusammenhang zwischen Optimismus und depressiven Symptomen
ist in allen Altersgruppen signifikant – unabhängig vom Alter #### Der
Zusammenhang wird nicht durch das Alter abgeschwächt oder verstärkt.
#### Es liegt keine bedeutsame Interaktion zwischen Optimismus und Alter
vor.
Anschauen, ob diesselben Dinge für Pessimismus gelten
cor.test(MIDUS$pessimism, MIDUS$cesd, method = "pearson")
##
## Pearson's product-moment correlation
##
## data: MIDUS$pessimism and MIDUS$cesd
## t = 9.8911, df = 605, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3024955 0.4396233
## sample estimates:
## cor
## 0.3730952
cor.test(MIDUS$pessimism, MIDUS$education, method = "pearson")
##
## Pearson's product-moment correlation
##
## data: MIDUS$pessimism and MIDUS$education
## t = -5.2829, df = 606, p-value = 1.776e-07
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2845928 -0.1325208
## sample estimates:
## cor
## -0.2098254
Auch bei Pessimismus besteht eine Korrelation zu Depression, die
signfikant ist und bei 0.37 liegt
Interessanterweise ist, im Gegensatz zu Optimismus, Pessimismus
signifikant mit Bildung korreliert und zwar zu -0.21
Anschauen der Interaktion mit Bildung
Variable zentrieren, Zentrierung ohne Standardisierung
MIDUS$pessimism_z <- scale(MIDUS$pessimism, scale = FALSE)
Hierarchische Regression
Dabei für depressive Symptome zum Zeitpunkt der Erhebung des
Optimismus kontrollieren
Modell 1: Hauptmodell ohne Interaktion
modell1_pes <- lm(cesd ~ pessimism_z + education_z +depressedaffect, data = MIDUS)
summary(modell1_pes)
##
## Call:
## lm(formula = cesd ~ pessimism_z + education_z + depressedaffect,
## data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.584 -4.378 -1.375 3.221 30.488
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.8029 0.2795 27.915 < 2e-16 ***
## pessimism_z 0.8017 0.1041 7.703 5.47e-14 ***
## education_z -0.1296 0.1147 -1.130 0.259
## depressedaffect 1.2435 0.1665 7.468 2.87e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.558 on 603 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.2131, Adjusted R-squared: 0.2092
## F-statistic: 54.42 on 3 and 603 DF, p-value: < 2.2e-16
standardize_parameters(modell1_pes)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## --------------------------------------------
## (Intercept) | -2.91e-16 | [-0.07, 0.07]
## pessimism z | 0.29 | [ 0.22, 0.37]
## education z | -0.04 | [-0.11, 0.03]
## depressedaffect | 0.28 | [ 0.21, 0.35]
tidy_mod1_pes <- broom::tidy(modell1_pes)
kable(tidy_mod1_pes, caption = "Regressionsoutput Modell 1")
Regressionsoutput Modell 1
| (Intercept) |
7.8029068 |
0.2795201 |
27.915369 |
0.0000000 |
| pessimism_z |
0.8016603 |
0.1040682 |
7.703222 |
0.0000000 |
| education_z |
-0.1296235 |
0.1147053 |
-1.130057 |
0.2589015 |
| depressedaffect |
1.2435092 |
0.1665162 |
7.467797 |
0.0000000 |
modell1.1_pes <- anova(modell1_pes)
kable(modell1.1_pes, caption = "ANOVA-Tabelle Modell 1")
ANOVA-Tabelle Modell 1
| pessimism_z |
1 |
4586.75851 |
4586.75851 |
106.6650690 |
0.0000000 |
| education_z |
1 |
36.07474 |
36.07474 |
0.8389182 |
0.3600725 |
| depressedaffect |
1 |
2398.10785 |
2398.10785 |
55.7679981 |
0.0000000 |
| Residuals |
603 |
25929.90757 |
43.00151 |
NA |
NA |
Modell 2: Modell mit Interaktion
modell2_pes <- lm(cesd ~ pessimism_z * education_z +depressedaffect, data = MIDUS)
summary(modell2_pes)
##
## Call:
## lm(formula = cesd ~ pessimism_z * education_z + depressedaffect,
## data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.638 -4.338 -1.338 3.184 30.490
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.82157 0.28418 27.524 < 2e-16 ***
## pessimism_z 0.80907 0.10603 7.631 9.18e-14 ***
## education_z -0.12907 0.11480 -1.124 0.261
## depressedaffect 1.24460 0.16666 7.468 2.88e-13 ***
## pessimism_z:education_z 0.01496 0.04018 0.372 0.710
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.562 on 602 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.2133, Adjusted R-squared: 0.208
## F-statistic: 40.79 on 4 and 602 DF, p-value: < 2.2e-16
standardize_parameters(modell2_pes)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## ------------------------------------------------------
## (Intercept) | 2.59e-03 | [-0.07, 0.07]
## pessimism z | 0.30 | [ 0.22, 0.37]
## education z | -0.04 | [-0.11, 0.03]
## depressedaffect | 0.28 | [ 0.21, 0.35]
## pessimism z × education z | 0.01 | [-0.06, 0.08]
tidy_mod2_pes <- broom::tidy(modell2_pes)
kable(tidy_mod2_pes, caption = "Regressionsoutput Modell 2")
Regressionsoutput Modell 2
| (Intercept) |
7.8215731 |
0.2841752 |
27.523767 |
0.0000000 |
| pessimism_z |
0.8090729 |
0.1060277 |
7.630771 |
0.0000000 |
| education_z |
-0.1290701 |
0.1147969 |
-1.124334 |
0.2613193 |
| depressedaffect |
1.2445993 |
0.1666610 |
7.467852 |
0.0000000 |
| pessimism_z:education_z |
0.0149645 |
0.0401829 |
0.372409 |
0.7097194 |
modell2.1_pes <- anova(modell2_pes)
kable(modell2.1_pes, caption = "ANOVA-Tabelle Modell 2")
ANOVA-Tabelle Modell 2
| pessimism_z |
1 |
4586.758509 |
4586.758509 |
106.5127111 |
0.0000000 |
| education_z |
1 |
36.074745 |
36.074745 |
0.8377199 |
0.3604162 |
| depressedaffect |
1 |
2398.107853 |
2398.107853 |
55.6883403 |
0.0000000 |
| pessimism_z:education_z |
1 |
5.972344 |
5.972344 |
0.1386885 |
0.7097194 |
| Residuals |
602 |
25923.935227 |
43.063015 |
NA |
NA |
Testen, ob das Modell mit Interaktion signifikant besser passt
modell_ges_pes <- anova(modell1_pes,modell2_pes)
kable(modell_ges_pes, caption = "ANOVA-Tabelle")
ANOVA-Tabelle
| 603 |
25929.91 |
NA |
NA |
NA |
NA |
| 602 |
25923.94 |
1 |
5.972344 |
0.1386885 |
0.7097194 |
r2_diff_pes <- summary(modell2_pes)$r.squared - summary(modell1_pes)$r.squared
cat("R²-Zuwachs durch Interaktion:", round(r2_diff_pes, 4))
## R²-Zuwachs durch Interaktion: 2e-04
=>Auch für Pessimismus ist die Interaktion mit Bildung nicht
signifikant
Hypothese 2a überprüfen
library(interactions)
slopes <- sim_slopes(modell2_pes, pred = "pessimism_z", modx = "education_z", johnson_neyman = FALSE)
slopes.table <- slopes$slopes
print(slopes.table)
## Value of education_z Est. S.E. 2.5% 97.5% t val.
## 1 -2.35890961 0.7737731 0.1282699 0.5218622 1.025684 6.032382
## 2 0.01220753 0.8092556 0.1061209 0.6008435 1.017668 7.625792
## 3 2.38332466 0.8447381 0.1556470 0.5390609 1.150415 5.427267
## p
## 1 2.821963e-09
## 2 9.504425e-14
## 3 8.305387e-08
Anschauen der Interaktion mit Alter
Hierarchische Regression
Dabei für depressive Symptome zum Zeitpunkt der Erhebung des
Optimismus kontrollieren
Modell 1: Hauptmodell ohne Interaktion
modell1_age_pes <- lm(cesd ~ pessimism_z + age_z + depressedaffect, data = MIDUS)
summary(modell1_age_pes)
##
## Call:
## lm(formula = cesd ~ pessimism_z + age_z + depressedaffect, data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.727 -4.407 -1.348 3.236 30.306
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.80964 0.27989 27.903 < 2e-16 ***
## pessimism_z 0.81689 0.10309 7.924 1.11e-14 ***
## age_z -0.01590 0.02794 -0.569 0.57
## depressedaffect 1.22974 0.16723 7.354 6.32e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.563 on 603 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.2118, Adjusted R-squared: 0.2079
## F-statistic: 54.02 on 3 and 603 DF, p-value: < 2.2e-16
standardize_parameters(modell1_age_pes)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## --------------------------------------------
## (Intercept) | -2.96e-16 | [-0.07, 0.07]
## pessimism z | 0.30 | [ 0.23, 0.37]
## age z | -0.02 | [-0.09, 0.05]
## depressedaffect | 0.28 | [ 0.20, 0.35]
tidy_mod1_age_pes <- broom::tidy(modell1_age_pes)
kable(tidy_mod1_age_pes, caption = "Regressionsoutput Modell 1")
Regressionsoutput Modell 1
| (Intercept) |
7.8096356 |
0.2798890 |
27.902614 |
0.0000000 |
| pessimism_z |
0.8168866 |
0.1030865 |
7.924285 |
0.0000000 |
| age_z |
-0.0158963 |
0.0279425 |
-0.568891 |
0.5696419 |
| depressedaffect |
1.2297375 |
0.1672269 |
7.353707 |
0.0000000 |
modell1.1_age_pes <- anova(modell1_age_pes)
kable(modell1.1_age_pes, caption = "ANOVA-Tabelle Modell 1")
ANOVA-Tabelle Modell 1
| pessimism_z |
1 |
4586.75851 |
4586.75851 |
106.496779 |
0.0000000 |
| age_z |
1 |
64.14006 |
64.14006 |
1.489224 |
0.2228139 |
| depressedaffect |
1 |
2329.06725 |
2329.06725 |
54.077005 |
0.0000000 |
| Residuals |
603 |
25970.88286 |
43.06946 |
NA |
NA |
Modell 2: Modell mit Interaktion
modell2_age_pes <- lm(cesd ~ pessimism_z * age_z + depressedaffect, data = MIDUS)
summary(modell2_age_pes)
##
## Call:
## lm(formula = cesd ~ pessimism_z * age_z + depressedaffect, data = MIDUS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.806 -4.406 -1.349 3.291 30.398
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.797128 0.283794 27.475 < 2e-16 ***
## pessimism_z 0.808395 0.107714 7.505 2.22e-13 ***
## age_z -0.017148 0.028334 -0.605 0.545
## depressedaffect 1.227905 0.167489 7.331 7.38e-13 ***
## pessimism_z:age_z -0.003029 0.011048 -0.274 0.784
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.568 on 602 degrees of freedom
## (15 observations deleted due to missingness)
## Multiple R-squared: 0.2119, Adjusted R-squared: 0.2067
## F-statistic: 40.47 on 4 and 602 DF, p-value: < 2.2e-16
standardize_parameters(modell2_age_pes)
## # Standardization method: refit
##
## Parameter | Std. Coef. | 95% CI
## ------------------------------------------------
## (Intercept) | -1.82e-03 | [-0.07, 0.07]
## pessimism z | 0.30 | [ 0.22, 0.37]
## age z | -0.02 | [-0.10, 0.05]
## depressedaffect | 0.28 | [ 0.20, 0.35]
## pessimism z × age z | -0.01 | [-0.09, 0.07]
tidy_mod2_age_pes <- broom::tidy(modell2_age_pes)
kable(tidy_mod2_age_pes, caption = "Regressionsoutput Modell 2")
Regressionsoutput Modell 2
| (Intercept) |
7.7971282 |
0.2837936 |
27.4746476 |
0.0000000 |
| pessimism_z |
0.8083946 |
0.1077138 |
7.5050261 |
0.0000000 |
| age_z |
-0.0171476 |
0.0283339 |
-0.6051979 |
0.5452756 |
| depressedaffect |
1.2279046 |
0.1674887 |
7.3312676 |
0.0000000 |
| pessimism_z:age_z |
-0.0030293 |
0.0110477 |
-0.2742043 |
0.7840217 |
modell2.1_age_pes <- anova(modell2_age_pes)
kable(modell2.1_age_pes, caption = "ANOVA-Tabelle Modell 2")
ANOVA-Tabelle Modell 2
| pessimism_z |
1 |
4586.758509 |
4586.758509 |
106.333447 |
0.0000000 |
| age_z |
1 |
64.140062 |
64.140062 |
1.486940 |
0.2231694 |
| depressedaffect |
1 |
2329.067248 |
2329.067248 |
53.994067 |
0.0000000 |
| pessimism_z:age_z |
1 |
3.243282 |
3.243282 |
0.075188 |
0.7840217 |
| Residuals |
602 |
25967.639576 |
43.135614 |
NA |
NA |
Testen, ob das Modell mit Interaktion signifikant besser passt
modell_ges_age_pes <- anova(modell1_age_pes,modell2_age_pes)
kable(modell_ges_age_pes, caption = "ANOVA-Tabelle")
ANOVA-Tabelle
| 603 |
25970.88 |
NA |
NA |
NA |
NA |
| 602 |
25967.64 |
1 |
3.243282 |
0.075188 |
0.7840217 |
r2_diff_age_pes <- summary(modell2_age_pes)$r.squared - summary(modell1_age_pes)$r.squared
cat("R²-Zuwachs durch Interaktion:", round(r2_diff_age_pes, 4))
## R²-Zuwachs durch Interaktion: 1e-04
=>Auch für Pessimismus ist die Interaktion nicht signifikant
Details zur verwendeten Software anzeigen lassen
version
## _
## platform aarch64-apple-darwin20
## arch aarch64
## os darwin20
## system aarch64, darwin20
## status
## major 4
## minor 5.0
## year 2025
## month 04
## day 11
## svn rev 88135
## language R
## version.string R version 4.5.0 (2025-04-11)
## nickname How About a Twenty-Six