--- title: "Dyadic Score Model (DSM)" author: "Pascal Küng" description: > Construction and interpretation of DSM predictor scores and contrasts, including their relationship to APIM effects for distinguishable dyads. bibliography: references.bib output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Dyadic Score Model (DSM)} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r, include = FALSE} knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) diagram_helper <- if (file.exists("diagram-helpers.Rinc")) { "diagram-helpers.Rinc" } else { file.path("vignettes", "diagram-helpers.Rinc") } sys.source(diagram_helper, envir = knitr::knit_global()) diagram_device <- .vignette_diagram_device() knitr::opts_chunk$set( dev = diagram_device, fig.ext = diagram_device, dev.args = list(bg = "transparent") ) ``` ```{r setup} library(dyadMLM) ``` ```{r internal-setup, include=FALSE} has_glmmTMB <- requireNamespace("glmmTMB", quietly = TRUE) dsm_fitted_alt <- "Fitted DSM diagram unavailable." ``` This vignette focuses on the Dyadic Score Model (DSM) for distinguishable dyads and its relationship to the distinguishable Actor-Partner Interdependence Model (APIM). The DSM expresses associations in terms of the dyad's shared level and the directional difference between partners [@iidaModelsInterdependentIndividuals2018]. For the broader package workflow and an overview of the available model-specific vignettes, including the [Actor-Partner Interdependence Model](apim.html) and [Dyad-Individual Model](dim.html), see the [online package overview](https://pascal-kueng.github.io/dyadMLM/). ## Preparing DSM Data A DSM requires an explicitly declared direction. This direction should be substantively meaningful when the directional coefficients are interpreted. Here, `c("female", "male")` defines every difference as female minus male. Here $X_{\mathrm{female}}$ and $X_{\mathrm{male}}$ denote provided support centered with the pooled mean from complete predictor pairs. `prepare_dyad_data()` creates the corresponding DSM dyad-mean column; using the original zero requires shifting it manually. ```{r prepare-cross-dsm} cross_dsm_data <- dyadMLM::prepare_dyad_data( dyads_cross, dyad = coupleID, member = personID, role = gender, predictors = provided_support, model_types = "dsm", # All three observed compositions in `dyads_cross` are detected and retained by # default. This example focuses on `female-male` dyads, so we restrict the # analysis here. keep_compositions = "female-male", dsm_role_order = c("female", "male") ) print(cross_dsm_data, n = 4) ``` With this notation, `dyadMLM` creates the equivalent coordinates: - `.provided_support_dyad_mean_gmc` $= \frac{X_{\mathrm{female}} + X_{\mathrm{male}}}{2}$ - `.provided_support_within_dyad_diff` $= X_{\mathrm{female}} - X_{\mathrm{male}}$ - `.dsm_role_contrast` $= +0.5$ for female and $-0.5$ for male. The common centering shift cancels from the signed difference. Both predictor scores are repeated on the member rows; the outcome remains unchanged. APIM GMC uses all retained non-missing values, whereas DSM uses complete pairs, so their constants may differ with one-sided missingness. ## Cross-Sectional Gaussian DSM For a cross-sectional Gaussian DSM, a correlated dyad random intercept and role-contrast slope represent unexplained outcome-level and outcome-difference variance. ```{r conceptual-dsm-diagram, echo=FALSE, fig.width=9, fig.height=4.8, out.width="100%", fig.cap="Conceptual cross-sectional DSM. Predictor mean and predictor difference each predict both outcome scores.", fig.alt="Path diagram for a cross-sectional dyadic score model. The centered female-male predictor mean and female-minus-male predictor difference each predict the female-male outcome mean and female-minus-male outcome difference. Paths are labelled a11, a12, a21, and a22, and outcome intercepts are labelled a10 and a20."} draw_dsm_diagram() ``` The same model can be displayed in the individual-member rows used by the long-format multilevel model. ```{r conceptual-dsm-member-diagram, echo=FALSE, fig.width=9, fig.height=5.6, out.width="100%", fig.cap="Individual-level representation of the cross-sectional DSM used for the long-format multilevel model. The centered predictor mean and female-minus-male predictor difference appear on both member rows. For the female outcome, the intercept and slopes add one-half of the corresponding outcome-difference parameters. For the male outcome, they subtract one-half. The female and male residuals may have different variances and covary.", fig.alt="Two-panel path diagram for a female-minus-male dyadic score model. Both panels contain the centered predictor mean and female-minus-male predictor difference. For the female outcome, the intercept is a10 plus half a20, the predictor-mean coefficient is a11 plus half a21, and the predictor-difference coefficient is a12 plus half a22. For the male outcome, the same combinations use minus signs. The two member residuals covary."} draw_dsm_member_diagram() ``` The path labels correspond directly to the terms in the model below: ```{r fit-cross-dsm, eval=has_glmmTMB} dsm_model <- glmmTMB::glmmTMB( closeness ~ # Outcome-level intercept 1 + # Predictor level -> outcome level (a11) .provided_support_dyad_mean_gmc + # Predictor difference -> outcome level (a12) .provided_support_within_dyad_diff + # Outcome-difference intercept (a20) .dsm_role_contrast + # Predictor level -> outcome difference (a21) .provided_support_dyad_mean_gmc:.dsm_role_contrast + # Predictor difference -> outcome difference (a22) .provided_support_within_dyad_diff:.dsm_role_contrast + # Outcome-level and outcome-difference residual variances and their covariance us(1 + .dsm_role_contrast | coupleID), dispformula = ~ 0, family = gaussian(), data = cross_dsm_data ) summary(dsm_model) ``` ### Interpreting the DSM paths For the outcomes given the predictors, the long-format model estimates the same paths as the conventional score-based DSM [@iidaModelsInterdependentIndividuals2018]. In the conventional score-based representation, the **predictors** are decomposed in the same way: $$ X_{\mathrm{mean}} = \frac{X_{\mathrm{female}} + X_{\mathrm{male}}}{2}, \qquad X_{\mathrm{diff}} = X_{\mathrm{female}} - X_{\mathrm{male}}. $$ Here the two member predictors already share the pooled grand-mean reference, so $X_{\mathrm{mean}}$ is grand-mean centered and the common shift cancels from $X_{\mathrm{diff}}$. The **outcomes** are also decomposed: $$ Y_{\mathrm{mean}} = \frac{Y_{\mathrm{female}} + Y_{\mathrm{male}}}{2}, \qquad Y_{\mathrm{diff}} = Y_{\mathrm{female}} - Y_{\mathrm{male}}. $$ The long-format model fitted here does not create $Y_{\mathrm{mean}}$ and $Y_{\mathrm{diff}}$ as observed variables. Instead, it uses the member-level outcome directly. With complete outcome pairs, this is an equivalent parameterization of the same conditional outcome regressions. Consider the conceptual SEM formulas: $$ \widehat{Y_{\mathrm{mean}}} = a_{10} + a_{11}X_{\mathrm{mean}} + a_{12}X_{\mathrm{diff}}, $$ $$ \widehat{Y_{\mathrm{diff}}} = a_{20} + a_{21}X_{\mathrm{mean}} + a_{22}X_{\mathrm{diff}}. $$ The fitted paths for this example are: ```{r prepare-fitted-dsm-diagram, include=FALSE, eval=has_glmmTMB} dsm_diagram_values <- .extract_dsm_diagram_values(dsm_model) dsm_diagram_estimates <- dsm_diagram_values$estimates dsm_diagram_residuals <- dsm_diagram_values$residuals dsm_fitted_alt <- sprintf( paste( "Fitted DSM. Intercepts a10 %.2f and a20 %.2f; paths a11 %.2f, a12 %.2f,", "a21 %.2f, and a22 %.2f; residual SDs %.2f and %.2f, with correlation %.2f." ), dsm_diagram_estimates[["a10"]], dsm_diagram_estimates[["a20"]], dsm_diagram_estimates[["a11"]], dsm_diagram_estimates[["a12"]], dsm_diagram_estimates[["a21"]], dsm_diagram_estimates[["a22"]], dsm_diagram_residuals[["sd_mean"]], dsm_diagram_residuals[["sd_difference"]], dsm_diagram_residuals[["correlation"]] ) ``` ```{r fitted-dsm-diagram, echo=FALSE, eval=has_glmmTMB, fig.width=9, fig.height=4.8, out.width="100%", fig.cap="Fitted cross-sectional DSM for the example data. The nodes identify the mean and difference scores; edge and intercept labels show the estimated DSM coefficients, and the residual labels show the estimated score-component standard deviations and correlation.", fig.alt=dsm_fitted_alt} draw_dsm_diagram( model = dsm_model, labels = c(predictor = "provided support", outcome = "closeness") ) ``` The fixed effects from our MLM model map directly to these paths as such: | Long-format fixed effect | DSM SEM path and interpretation | |---|---| | Intercept | $a_{10}$: expected dyad-average closeness at the sample-average provided-support level and no female-male support difference | | Provided-support dyad mean | $a_{11}$: predictor level $\rightarrow$ outcome level | | Provided-support difference | $a_{12}$: predictor difference $\rightarrow$ outcome level | | DSM role contrast | $a_{20}$: expected female-minus-male outcome difference at the predictor reference values | | Dyad mean $\times$ role contrast | $a_{21}$: predictor level $\rightarrow$ outcome difference | | Provided-support difference $\times$ role contrast | $a_{22}$: predictor difference $\rightarrow$ outcome difference | Thus, for example, $a_{12}$ is the change in dyad-average closeness associated with a one-unit larger female-minus-male provided-support difference, holding support level constant. In contrast, $a_{22}$ is the change in the female-minus-male closeness difference associated with that same one-unit larger support difference, holding support level constant. The $a_{12}$ and $a_{21}$ coefficients are the DSM cross-paths. They are omitted from the reduced DSM but are needed for the full model. The random intercept variance is unexplained variance in outcome level, and the random role-contrast slope variance is unexplained variance in the full directional outcome difference. Their covariance indicates whether unexplained outcome level and unexplained outcome difference are associated. The curved arrow $\rho_{r_m r_d}$ is the scale-free correlation between the outcome-mean residual and the outcome-difference residual. It is **not** the female-male residual correlation $\rho_{\epsilon_F\epsilon_M}$ from the APIM. The DSM uses the full female-minus-male difference: $$ e_{\mathrm{F}} = r_{\mathrm{m}} + \frac{1}{2}r_{\mathrm{d}}, \qquad e_{\mathrm{M}} = r_{\mathrm{m}} - \frac{1}{2}r_{\mathrm{d}}. $$ Therefore, this relationship applies: $$ \operatorname{Cov}(r_{\mathrm{m}},r_{\mathrm{d}}) = \frac{\operatorname{Var}(e_{\mathrm{F}})-\operatorname{Var}(e_{\mathrm{M}})}{2}. $$ For this reason, a nonzero $\rho_{r_m r_d}$ indicates that the two roles have different residual variances. The remaining covariance between the partners' residuals is $$ \operatorname{Cov}(e_{\mathrm{F}},e_{\mathrm{M}}) = \operatorname{Var}(r_{\mathrm{m}})-\frac{1}{4}\operatorname{Var}(r_{\mathrm{d}}). $$ ### Reversing the coding Instead of computing $X_{\mathrm{female}} - X_{\mathrm{male}}$, we can reverse the direction and compute $X_{\mathrm{male}} - X_{\mathrm{female}}$. This changes the direction of the differences, but not the substantive model. ```{r prepare-cross-dsm-inverted} cross_dsm_data_inverted <- dyadMLM::prepare_dyad_data( dyads_cross, dyad = coupleID, member = personID, role = gender, predictors = provided_support, # Request APIM columns too for comparison below. model_types = c("dsm", "apim"), add_apim_gmc_predictors = TRUE, keep_compositions = "female-male", dsm_role_order = c("male", "female") ) ``` ```{r fit-cross-dsm-inverted, eval=has_glmmTMB} dsm_model_inverted <- glmmTMB::glmmTMB( closeness ~ .provided_support_dyad_mean_gmc + .provided_support_within_dyad_diff + .dsm_role_contrast + .provided_support_dyad_mean_gmc:.dsm_role_contrast + .provided_support_within_dyad_diff:.dsm_role_contrast + us(1 + .dsm_role_contrast | coupleID), dispformula = ~ 0, family = gaussian(), data = cross_dsm_data_inverted ) female_minus_male <- glmmTMB::fixef(dsm_model)$cond male_minus_female <- glmmTMB::fixef(dsm_model_inverted)$cond knitr::kable( data.frame( `model term` = names(female_minus_male), `female - male` = unname(female_minus_male), `male - female` = unname(male_minus_female), check.names = FALSE ), digits = 3, align = c("l", "r", "r") ) ``` The two models have identical fitted values and model fit: - `.provided_support_within_dyad_diff` reverses because the predictor difference reverses. - `.dsm_role_contrast` reverses because the represented outcome difference reverses. - `.provided_support_dyad_mean_gmc:.dsm_role_contrast` reverses because only the outcome difference reverses. - `.provided_support_within_dyad_diff:.dsm_role_contrast` remains unchanged because both differences reverse. The intercept and `.provided_support_dyad_mean_gmc` also remain unchanged. For the random effects, the variances of `(Intercept)` and `.dsm_role_contrast` remain unchanged, whereas their covariance reverses sign. ## Relationship to the APIM and DIM For distinguishable dyads, the full DSM and an unconstrained distinguishable APIM are alternative parameterizations of the same fixed associations [@iidaModelsInterdependentIndividuals2018]. Let's fit the equivalent distinguishable APIM: ```{r fit-cross-apim, eval=has_glmmTMB} apim_model <- glmmTMB::glmmTMB( closeness ~ # Role-specific intercepts 0 + .is_female + .is_male + # Role-specific actor effects .is_female:.provided_support_gmc_actor + .is_male:.provided_support_gmc_actor + # Role-specific partner effects .is_female:.provided_support_gmc_partner + .is_male:.provided_support_gmc_partner + # Role-specific Gaussian residual covariance structure us(0 + .is_female + .is_male | coupleID), dispformula = ~ 0, family = gaussian(), data = cross_dsm_data_inverted ) ``` The two DSM directions and the APIM have identical fit statistics: ```{r compare-cross-fit, eval=has_glmmTMB} data.frame( model = c("DSM: female - male", "DSM: male - female", "APIM"), AIC = round(c(AIC(dsm_model), AIC(dsm_model_inverted), AIC(apim_model)), 3), BIC = round(c(BIC(dsm_model), BIC(dsm_model_inverted), BIC(apim_model)), 3), logLik = round(c( as.numeric(logLik(dsm_model)), as.numeric(logLik(dsm_model_inverted)), as.numeric(logLik(apim_model)) ), 3) ) ``` ### Fixed-effect transformation Let $b_{\mathrm{actor},\mathrm{female}}$ and $b_{\mathrm{actor},\mathrm{male}}$ denote the actor effects on the female and male outcomes. The corresponding partner effects are $b_{\mathrm{partner},\mathrm{female}}$ and $b_{\mathrm{partner},\mathrm{male}}$, and the APIM intercepts are $b_{0,\mathrm{female}}$ and $b_{0,\mathrm{male}}$. Fixed APIM coefficients use $b$ and write out their effect and outcome role. The numbered paths $a_{10}$ through $a_{22}$ retain the published DSM notation. The slope transformation can be understood in two steps. First, for each outcome role $r \in \{\mathrm{female},\mathrm{male}\}$, form the actor-plus-partner and actor-minus-partner combinations: $$ \begin{aligned} b_{\mathrm{sum},r} &= b_{\mathrm{actor},r} + b_{\mathrm{partner},r}, \\ b_{\mathrm{difference},r} &= b_{\mathrm{actor},r} - b_{\mathrm{partner},r}. \end{aligned} $$ The DSM slopes then follow by combining the female- and male-outcome effects: $$ \begin{aligned} a_{11} &= \frac{b_{\mathrm{sum},\mathrm{female}} + b_{\mathrm{sum},\mathrm{male}}}{2}, & a_{21} &= b_{\mathrm{sum},\mathrm{female}} - b_{\mathrm{sum},\mathrm{male}}, \\ a_{12} &= \frac{b_{\mathrm{difference},\mathrm{female}} - b_{\mathrm{difference},\mathrm{male}}}{4}, & a_{22} &= \frac{b_{\mathrm{difference},\mathrm{female}} + b_{\mathrm{difference},\mathrm{male}}}{2}. \end{aligned} $$ With complete pairs, the GMC APIM and DSM share a zero point, so the intercepts transform as $$ a_{10} = \frac{b_{0,\mathrm{female}} + b_{0,\mathrm{male}}}{2}, \qquad a_{20} = b_{0,\mathrm{female}} - b_{0,\mathrm{male}}. $$ Raw APIM predictors leave the slope transformations unchanged but require intercept recentering. For the reverse slope transformation, first recover the role-specific actor-plus-partner and actor-minus-partner combinations: $$ \begin{aligned} b_{\mathrm{sum},\mathrm{female}} &= a_{11} + \frac{a_{21}}{2}, & b_{\mathrm{sum},\mathrm{male}} &= a_{11} - \frac{a_{21}}{2}, \\ b_{\mathrm{difference},\mathrm{female}} &= a_{22} + 2a_{12}, & b_{\mathrm{difference},\mathrm{male}} &= a_{22} - 2a_{12}. \end{aligned} $$ Then, for each outcome role $r$, $$ b_{\mathrm{actor},r} = \frac{b_{\mathrm{sum},r} + b_{\mathrm{difference},r}}{2}, \qquad b_{\mathrm{partner},r} = \frac{b_{\mathrm{sum},r} - b_{\mathrm{difference},r}}{2}. $$ The intercepts transform back as $$ b_{0,\mathrm{female}} = a_{10} + \frac{a_{20}}{2}, $$ $$ b_{0,\mathrm{male}} = a_{10} - \frac{a_{20}}{2}. $$ The following comparison applies the APIM-to-DSM transformation to all six fixed effects: ```{r compare-cross-coefficients, eval=has_glmmTMB, echo=FALSE} apim_coef <- glmmTMB::fixef(apim_model)$cond dsm_coef <- glmmTMB::fixef(dsm_model)$cond b0_female <- apim_coef[[".is_female"]] b0_male <- apim_coef[[".is_male"]] b_actor_female <- apim_coef[[ ".is_female:.provided_support_gmc_actor" ]] b_actor_male <- apim_coef[[ ".is_male:.provided_support_gmc_actor" ]] b_partner_female <- apim_coef[[ ".is_female:.provided_support_gmc_partner" ]] b_partner_male <- apim_coef[[ ".is_male:.provided_support_gmc_partner" ]] b_sum_female <- b_actor_female + b_partner_female b_sum_male <- b_actor_male + b_partner_male b_difference_female <- b_actor_female - b_partner_female b_difference_male <- b_actor_male - b_partner_male a11_from_apim <- (b_sum_female + b_sum_male) / 2 a21_from_apim <- b_sum_female - b_sum_male a12_from_apim <- (b_difference_female - b_difference_male) / 4 a22_from_apim <- (b_difference_female + b_difference_male) / 2 apim_to_dsm <- c( a10 = (b0_female + b0_male) / 2, a11 = a11_from_apim, a12 = a12_from_apim, a20 = b0_female - b0_male, a21 = a21_from_apim, a22 = a22_from_apim ) a10_dsm <- dsm_coef[["(Intercept)"]] a11_dsm <- dsm_coef[[".provided_support_dyad_mean_gmc"]] a12_dsm <- dsm_coef[[".provided_support_within_dyad_diff"]] a20_dsm <- dsm_coef[[".dsm_role_contrast"]] a21_dsm <- dsm_coef[[ ".provided_support_dyad_mean_gmc:.dsm_role_contrast" ]] a22_dsm <- dsm_coef[[ ".provided_support_within_dyad_diff:.dsm_role_contrast" ]] knitr::kable( data.frame( `DSM path` = names(apim_to_dsm), `From APIM transformation` = round(unname(apim_to_dsm), 3), `From DSM model` = round(c( a10_dsm, a11_dsm, a12_dsm, a20_dsm, a21_dsm, a22_dsm ), 3), check.names = FALSE ), align = c("l", "r", "r"), caption = paste( "APIM-to-DSM fixed-effect transformation with pooled", "grand-mean-centered actor and partner predictors." ) ) ``` ### Random-effect transformation Let $u_{\mathrm{female}}$ and $u_{\mathrm{male}}$ be the APIM random effects for the female and male outcomes. The DSM outcome-level and outcome-difference residuals are the same random effects expressed in different coordinates: $$ \begin{pmatrix} r_{Y,\mathrm{mean}} \\ r_{Y,\mathrm{diff}} \end{pmatrix} = \begin{pmatrix} 1/2 & 1/2 \\ 1 & -1 \end{pmatrix} \begin{pmatrix} u_{\mathrm{female}} \\ u_{\mathrm{male}} \end{pmatrix}. $$ Applying this rotation to the APIM covariance matrix reproduces the DSM random intercept variance, intercept-slope covariance, and role-slope variance: ```{r compare-cross-random-effects, eval=has_glmmTMB} apim_vcov <- as.matrix(glmmTMB::VarCorr(apim_model)$cond$coupleID) dsm_vcov <- as.matrix(glmmTMB::VarCorr(dsm_model)$cond$coupleID) rotation <- rbind( outcome_level = c(0.5, 0.5), outcome_difference = c(1, -1) ) apim_to_dsm_vcov <- rotation %*% apim_vcov %*% t(rotation) data.frame( parameter = c( "Var(outcome mean)", "Cov(outcome mean, outcome diff)", "Var(outcome diff)" ), from_DSM = round(c( dsm_vcov[1, 1], dsm_vcov[1, 2], dsm_vcov[2, 2] ), 3), from_APIM_transformation = round(c( apim_to_dsm_vcov[1, 1], apim_to_dsm_vcov[1, 2], apim_to_dsm_vcov[2, 2] ), 3) ) ``` For exchangeable dyads, the direction of a member difference is arbitrary. The directional intercept, both cross-paths, and the covariance between outcome level and outcome difference must then be zero. The remaining reduced, label-invariant DSM is algebraically the Gaussian Dyad-Individual Model (DIM). In `dyadMLM`, use `model_types = "dim"` for this exchangeable model and reserve `model_types = "dsm"` for distinguishable dyads. Because the Gaussian DIM is the exchangeability-constrained version of the full DSM, exchangeability can also be tested by comparing these nested models. This is equivalent to the comparison shown in [Testing distinguishability in the APIM vignette](apim.html#testing-distinguishability). ## Checking partner dependence We can check whether the fitted DSM reproduces each role's response variance and the partner correlation by comparing observed and simulated data. ::: {.no-invert-dark-mode} ```{r check-cross-dsm, dev.args = list(bg = "white"), eval = has_glmmTMB, fig.width = 10, fig.height = 6.5, out.width = "100%", fig.alt = "Six predictive-check histograms for the DSM. Member SDs and partner correlation are in the top row; dyad-average and half-difference summaries are in the bottom row. Red lines mark observed values."} dsm_simulations <- dyadMLM::simulate_dyad_responses(dsm_model, seed = 123) dyadMLM::check_partner_dependence( dsm_simulations, dyad = coupleID, role = gender, # Supply the fitting data because gender is not in the model formula. data = cross_dsm_data ) ``` ::: The top row shows role-specific SDs and partner correlation. The bottom row shows the same information using dyad averages and half the differences between partners. Histograms show simulated values and red lines mark observed values. A red line far from most simulations suggests a mismatch. By default, the check subtracts the model's fixed-effect predictions from observed and simulated responses. Good agreement is often expected for variances and correlations estimated from the same data. See the [function help](https://pascal-kueng.github.io/dyadMLM/reference/check_partner_dependence.html) for details and interpretation. Simulation studies show how often the check detects [omitted partner dependence](https://pascal-kueng.github.io/dyadMLM/articles/partner-dependence-simulation.html) and [incorrect covariance pooling](https://pascal-kueng.github.io/dyadMLM/articles/covariance-pooling.html), and how often it raises false alarms. For intensive longitudinal data, also supply `member` and `time`. A [separate study](https://pascal-kueng.github.io/dyadMLM/articles/ild-partner-dependence.html) covers this case. The same `dsm_simulations` can be checked with [`check_dyad_residuals()`](https://pascal-kueng.github.io/dyadMLM/reference/check_dyad_residuals.html) and [`check_dyad_outcomes()`](https://pascal-kueng.github.io/dyadMLM/reference/check_dyad_outcomes.html), as shown in the [APIM vignette](apim.html#checking-residuals-and-outcomes). ## Intensive longitudinal DSM The intensive longitudinal DSM extends the cross-sectional DSM using the same temporal decomposition and multilevel workflow shown for the [intensive longitudinal DIM](dim.html#intensive-longitudinal-dim). The DSM retains the directional mean-and-difference parameterization described above. For more detail on centering decisions and mean-and-deviation interpretation, refer to the [DIM vignette](dim.html#intensive-longitudinal-dim). For dynamic models and their cautions, see the [dynamic ILD APIM example](apim.html#dynamic-models). Brief example of ILD DSM: ```{r prepare-ild-dsm} ild_dsm_data <- dyadMLM::prepare_dyad_data( dyads_ild, dyad = coupleID, member = personID, role = gender, time = diaryday, predictors = provided_support, model_types = "dsm", keep_compositions = "female-male", dsm_role_order = c("female", "male") ) print(ild_dsm_data, n = 4) ``` The specification below estimates same-day associations between support and closeness and allows separate linear trends for the outcome level and the female-minus-male outcome difference. It also includes the role-specific AR(1) components specified and interpreted in the APIM vignette. ```{r fit-ild-dsm, eval = has_glmmTMB} dsm_ILD <- glmmTMB::glmmTMB( closeness ~ # Outcome-level intercept and linear time trend 1 + diaryday + # Within-person predictor level -> outcome level .provided_support_cwp_dyad_mean + # Within-person predictor difference -> outcome level .provided_support_cwp_within_dyad_diff + # Between-person predictor level -> outcome level .provided_support_cbp_dyad_mean + # Between-person predictor difference -> outcome level .provided_support_cbp_within_dyad_diff + # Outcome-difference intercept and linear time trend .dsm_role_contrast + diaryday:.dsm_role_contrast + # Within-person predictor level and difference -> outcome difference .provided_support_cwp_dyad_mean:.dsm_role_contrast + .provided_support_cwp_within_dyad_diff:.dsm_role_contrast + # Between-person predictor level and difference -> outcome difference .provided_support_cbp_dyad_mean:.dsm_role_contrast + .provided_support_cbp_within_dyad_diff:.dsm_role_contrast + # Stable outcome-level and outcome-difference covariance us(1 + .dsm_role_contrast | coupleID) + # Same-day outcome-level and outcome-difference covariance us(1 + .dsm_role_contrast | coupleID:diaryday) + # Role-specific residual persistence ar1(0 + .is_female:factor(diaryday) | coupleID) + ar1(0 + .is_male:factor(diaryday) | coupleID), dispformula = ~ 0, family = gaussian(), data = ild_dsm_data, # Non-default settings help this example converge. control = glmmTMB::glmmTMBControl( profile = TRUE, optimizer = stats::optim, optArgs = list(method = "BFGS") ) ) glmmTMB::VarCorr(dsm_ILD) ``` This AR-adjusted, fixed-slope DSM omits the actor random slopes present in the simulation. See the [distinguishable APIM AR(1) section](apim.html#distinguishable-residual-ar1) for the corresponding specification and interpretation. The cross-sectional path interpretation therefore applies separately at the within-person and between-person levels. At each level, the predictor dyad mean and directional difference predict both the outcome level and the directional outcome difference. --- Return to the [Actor-Partner Interdependence Model vignette](apim.html), see the [Dyad-Individual Model vignette](dim.html) for a related model specification, or return to the [online package overview](https://pascal-kueng.github.io/dyadMLM/). ## References ::: {#refs} :::