'CoviFam-study - Links between PFB-K, PSS-10, & PBQ-16'
(AsPredicted #65337)

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1) Have any data been collected for this study already?
It's complicated. We have already collected some data but explain in Question 8 why readers may consider this a valid pre-registration nevertheless.

2) What's the main question being asked or hypothesis being tested in this study?
We expect couple relationship satisfaction, perceived stress, and impaired parental bonding to be positively and reciprocally related to each other.
Cross-Lagged Panel Hypotheses:
H 1: Higher couple relationship satisfaction at Time 1 predicts higher couple relationship satisfaction at Time 2 (β1 > 0).
H 2: Higher couple relationship satisfaction at Time 1 predicts lower perceived stress at Time 2 (β2 < 0).
H 3: Higher couple relationship satisfaction at Time 1 predicts lower impaired parental bonding at Time 2 (β3 > 0).
H 4: Lower perceived stress at Time 1 predicts higher couple relationship satisfaction at Time 2 (β4 < 0).
H 5: Lower perceived stress at Time 1 predicts lower perceived stress at Time 2 (β5 > 0).
H 6: Lower perceived stress at Time 1 predicts lower impaired parental bonding at Time 2 (β6 > 0).
H 7: Lower impaired parental bonding at Time 1 predicts higher couple relationship satisfaction at Time 2 (β7 < 0).
H 8: Lower impaired parental bonding at Time 1 predicts lower perceived stress at Time 2 (β8 > 0).
H 9: Lower impaired parental bonding at Time 1 predicts lower impaired parental bonding at Time 2 (β9 > 0).
H 10: Couple relationship satisfaction and perceived stress negatively correlate at Time 1 (r1 < 0).
H 11: Perceived stress and impaired parental bonding positively correlate at Time 1 (r2 > 0).
H 12: Couple relationship satisfaction and impaired parental bonding negatively correlate at Time 1 (r3 < 0).
H 13: Couple relationship satisfaction and perceived stress negatively correlate at Time 2 (r4 < 0).
H 14: Perceived stress and impaired parental bonding positively correlate at Time 2 (r5 > 0).
H 15: Couple relationship satisfaction and impaired parental bonding negatively correlate at Time 2 (r6 < 0).
Our global alpha level is .05. The panel analysis is run via forced entry in our structural equation model which is why H 1 - H 15 are considered independent, rendering a correction for multiple testing unnecessary. We rely on the p-values using Hochberg's False Discovery Rate (FDR) correction (Benjamini & Hochberg, 1995).

3) Describe the key dependent variable(s) specifying how they will be measured.
The three variables (1) couple relationship satisfaction, (2) perceived stress, and (3) impaired parental bonding were assessed as part of a larger longitudinal online survey in a community sample of parents with children between 0 and 3 years in Germany, Austria, and Switzerland (T 1: total N = 1951 between May and November 2020; T 2: total N = 772 between mid-February and mid-March 2021). For our main analyses (H 1 - H 15), we will only include mothers in our cross-lagged panel model.
To assess couple relationship satisfaction, the abridged version of the German partnership questionnaire "Partnerschaftsfragebogen" (PFB-K; Hahlweg, 2016) was applied. Nine of its ten items describe a partner's behavior within the relationship or mutual couple behavior. Participants were asked to indicate how often such behavior occurs in their relationships on a 5-point Likert-scale from "never/very rarely" to "very often". Their responses were coded from 0 to 4, respectively. A tenth item assessed overall couple relationship satisfaction on a 6-point Likert-scale. It was coded from 0 to 5 ("very unhappy" to "very happy"). This tenth item is not part of the sum score and was excluded from further analysis. The PFB-K consists of three sub-scales "Streit" (disagreement), "Zärtlichkeit" (affectionateness) and "Kommunikation" (communication). An overall sum score was calculated as follows: [(9-disagreement) + affectionateness + communication] (Halweg, 2016). Higher overall sum scores indicated higher couple relationship satisfaction. Standard values of a representative German sample are available in the manual referring to Kliem et al.'s scaling of the PFB-K from 2012.
Individuals' self-reported perceived stress was assessed using the German version of the Perceived Stress Scale (PSS-10; see Reis et al., 2019, for further information) which consists of 10 items and is answered on a 5-point Likert-scale which was coded from 0 to 4 ("never" to "very often"). We are interested in an overall impression of how strained a person is, which is why we will rely on the unidimensional sum score of the scale. The higher the sum score, the more stressed the participant is.
To assess impaired parental bonding, we applied the German version of the Postpartum Bonding Questionnaire (PBQ-16; Reck et al., 2006)), originally developed by Brockington et al. (2001). The 16-items are scored on a 6-point Likert-scale. Items stating positive feelings and sensations are coded from 0 ("always") to 5 ("never"). Items stating negative feelings and sensations were inverse items and coded from 5 ("always") to 0 ("never"). Higher sum scores represent more impaired bonding, implying that lower sum scores represent stronger parental bonding. For the 16-item version of the PBQ, Reck et al. (2006) report a Cronbach's alpha of 0.85.

4) How many and which conditions will participants be assigned to?
NA

5) Specify exactly which analyses you will conduct to examine the main question/hypothesis.
We will employ structural equation modelling in R (R Core Team, 2019) using the package "lavaan" (Rosseel, 2012). Parameter estimates will be obtained by a maximum-likelihood estimation with robust estimators of model fit (MLR) with robust (Huber-White) standard errors and a scaled test statistic that is (asymptotically) equal to the Yuan-Bentler test statistic as it is robust against the violation of normal distribution (Rosseel, 2020). A full-information maximum-likelihood (FIML) approach will be applied to compensate for missing data. To evaluate the quality of model fits, we will inspect a range of fit indices, including the comparative fit index (CFI), the Tucker Lewis Index (TLI; also called the non-normed fit index), the root-mean-square error of approximation (RMSEA), and the standardized root-mean-square residual (SRMR). In line with Hu & Bentler (1999), model fit will be interpreted as satisfactory when the CFI is above .90 and as excellent when above .95. The TLI indicates a good fit above a value of .95 (Hu & Bentler, 1999). The RMSEA demonstrates a good fit for values below .06, a moderate fit for values between .06 and .08, and a poor fit for values above .08 (Hu & Bentler, 1999). The SRMR shows a good fit below .08 (Hu & Bentler, 1999; see also Little & Kline, 2016).
As our main analysis, we will employ a cross-lagged panel design. We will test and compare four competing pathway models to assess unidirectional and/or bidirectional relations among the variables (Selig & Little, 2012): (1) stability model, including autoregressive effects (β1, β5, and β9), (2) pathway model, including autoregressive effects and the cross-lagged effect from couple relationship satisfaction to perceived stress and parental bonding as well as from perceived stress to parental bonding (β1, β2, β3, β5, β6, and β9), (3) reverse-pathway model, including autoregressive effects and the cross-lagged effect from parental bonding to couple relationship satisfaction and perceived stress as well as from perceived stress to couple relationship satisfaction (β1, β4, β5, β7, β8, and β9), and (4) reciprocal model, including autoregressive and all cross-lagged effects (β1-9). The correlations of the three manifest variables assessed at T1 and T2 (r1-6) were specified in model (2) - (4). In order to determine the best-fitting model, we will compare model (2) - (4) to the baseline model (1) by applying the AIC. Models will be regarded as considerably different with a difference of the AIC values between 4 and 7 and as essentially different with a difference of higher than 7, with the lower value model among models 2, 3 and 4 being accepted in such a case (Burnham & Anderson, 2002, p. 70). The first model is considered a baseline model for comparisons to be based on. Reproducible scripts and data will be accessible on the Open Science Framework.

6) Describe exactly how outliers will be defined and handled, and your precise rule(s) for excluding observations.
Since a FIML approach is utilized, no participants will be excluded, including outliers. We will exclude participants from Austria and Switzerland, because only a few individuals from these countries (< 100) participated in our online survey and we would like to focus on a more homogenous, German sample as restrictions were quite different across these countries.

7) How many observations will be collected or what will determine sample size?
No need to justify decision, but be precise about exactly how the number will be determined.
We will not know our final sample size until initial analyses will have been run to identify the number of eligible participant responses. However, our highest possible N can be estimated using the number of participant responses in the existing dataset of the second measurement point (N = 772).

8) Anything else you would like to pre-register?
(e.g., secondary analyses, variables collected for exploratory purposes, unusual analyses planned?)
We offered the online survey link of the CoviFam-Project (LMU Munich and University of Mannheim) from May 2020 till November 2020 since regulations were relaxed during this time. We reopened the online survey link and recontacted participants of the first wave in February and March 2021 during a time of shut-down. Data collection is finished. However, access to the data for the authors and statisticians will first be granted after pre-registration.
Several sociodemographic measures will be reported in descriptive statistics. Comparisons between fathers and mothers regarding the reported couple relationship satisfaction, parental bonding and perceived stress as well as comparisons between single parents vs. being in a relationship regarding parental bonding and perceived stress will be analyzed.

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