# multordRS: Model Multivariate Ordinal Responses Including Response... In MultOrdRS: Model Multivariate Ordinal Responses Including Response Styles

## Description

A model for multivariate ordinal responses. The response is modelled using a mixed model approach that is also capable of the inclusion of response style effects of the respondents.

## Usage

 ```1 2 3 4 5 6 7``` ```multordRS( formula, data = NULL, control = ctrl.multordRS(), se = TRUE, model = c("acat", "cumulative") ) ```

## Arguments

 `formula` Formula containing the (multivariate) ordinal response on the left side and the explanatory variables on the right side. `data` Data frame containing the ordinal responses as well as the explanatory variables from the `formula`. `control` Control argument for `multord()` function. For details see `ctrl.multordRS`. `se` Should standard errors be calculated for the regression coefficients? Default is `TRUE`. `model` Specifies, which type of model is used, either the (multivariate) adjacent categories model (`model = "acat"`) or the (multivariate) cumulative model (`model = "cumulative"`).

## Value

 `beta.thresh` Matrix containing all threshold parameters for the respective model. `beta.shift` Vector containing all shift parameters. Only relevant if `model = "acat"` and `thresholds.acat = "shift"`. `beta.X` Vector containing parameter estimates for the location effects of the explanatory variables. `beta.XRS` Vector containing parameter estimates for the response style effects of the explanatory variables. `Sigma` Estimate of the variance (or covariance matrix) of the random effects. The estimate is a matrix if person-specific random response style effects are considered in the model (i.e. if `RS = TRUE`). `Y` Matrix containing the explanatory variables. `X` Data frame containing the multivariate ordinal response, one row per obeservation, one column per response variable. `se.thresh` Matrix containing all standard errors of the threshold parameters for the respective model. `se.shift` Vector containing all standard errors of the shift parameters. Only relevant if `model = "acat"` and `thresholds.acat = "shift"`. `se.X` Vector containing standard errors of the parameter estimates for the location effects of the explanatory variables. `se.XRS` Vector containing standard errors of the parameter estimates for the response style effects of the explanatory variables. `coef.vec` Complete vector of all parameter estimates (for internal use). `se.vec` Complete vector of all standard errors (for internal use). `design.values` Some values of the design matrix (for internal use). `loglik` (Marginal) Log Likelihood `call` Function call `df` Degrees of freedom `control` Control argument from function call

## Author(s)

Gunther Schauberger
gunther.schauberger@tum.de
https://orcid.org/0000-0002-0392-1580

## References

Schauberger, Gunther and Tutz, Gerhard (2021): Multivariate Ordinal Random Effects Models Including Subject and Group Specific Response Style Effects, Statistical Modelling, https://journals.sagepub.com/doi/10.1177/1471082X20978034

`ctrl.multordRS` `MultOrdRS-package` `plot.MultOrdRS`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114``` ```data(tenseness) ## create a small subset of the data to speed up calculations set.seed(1860) tenseness <- tenseness[sample(1:nrow(tenseness), 300),] ## scale all metric variables to get comparable parameter estimates tenseness\$Age <- scale(tenseness\$Age) tenseness\$Income <- scale(tenseness\$Income) ## two formulas, one without and one with explanatory variables (gender and age) f.tense0 <- as.formula(paste("cbind(",paste(names(tenseness)[1:4],collapse=","),") ~ 1")) f.tense1 <- as.formula(paste("cbind(",paste(names(tenseness)[1:4],collapse=","),") ~ Gender + Age")) #### ## Adjacent Categories Models #### ## Multivariate adjacent categories model, without response style, without explanatory variables m.tense0 <- multordRS(f.tense0, data = tenseness, control = ctrl.multordRS(RS = FALSE, cores = 2)) m.tense0 ## Multivariate adjacent categories model, with response style as a random effect, ## without explanatory variables m.tense1 <- multordRS(f.tense0, data = tenseness) m.tense1 ## Multivariate adjacent categories model, with response style as a random effect, ## without explanatory variables for response style BUT for location m.tense2 <- multordRS(f.tense1, data = tenseness, control = ctrl.multordRS(XforRS = FALSE)) m.tense2 ## Multivariate adjacent categories model, with response style as a random effect, with ## explanatory variables for location AND response style m.tense3 <- multordRS(f.tense1, data = tenseness) m.tense3 plot(m.tense3) #### ## Cumulative Models #### ## Multivariate cumulative model, without response style, without explanatory variables m.tense0.cumul <- multordRS(f.tense0, data = tenseness, control = ctrl.multordRS(RS = FALSE), model = "cumulative") m.tense0.cumul ## Multivariate cumulative model, with response style as a random effect, ## without explanatory variables m.tense1.cumul <- multordRS(f.tense0, data = tenseness, model = "cumulative") m.tense1.cumul ## Multivariate cumulative model, with response style as a random effect, ## without explanatory variables for response style BUT for location m.tense2.cumul <- multordRS(f.tense1, data = tenseness, control = ctrl.multordRS(XforRS = FALSE), model = "cumulative") m.tense2.cumul ## Multivariate cumulative model, with response style as a random effect, with ## explanatory variables for location AND response style m.tense3.cumul <- multordRS(f.tense1, data = tenseness, model = "cumulative") m.tense3.cumul plot(m.tense3.cumul) ################################################################ ## Examples from Schauberger and Tutz (2020) ## Data from the German Longitudinal Election Study (GLES) 2017 ################################################################# #### ## Source: German Longitudinal Election Study 2017 ## Rossteutscher et al. 2017, https://doi.org/10.4232/1.12927 #### ## load GLES data data(GLES17) ## scale data GLES17[,7:11] <- scale(GLES17[,7:11]) ## define formula f.GLES <- as.formula(cbind(RefugeeCrisis, ClimateChange, Terrorism, Globalization, Turkey, NuclearEnergy) ~ Age + Gender + Unemployment + EastWest + Abitur) ## fit adjacent categories model without and with response style parameters m.GLES0 <- multordRS(f.GLES, data = GLES17, control = ctrl.multordRS(RS = FALSE, cores = 6)) m.GLES <- multordRS(f.GLES, data = GLES17, control = ctrl.multordRS(cores = 6)) m.GLES0 m.GLES plot(m.GLES, main = "Adjacent categories model") ## fit cumulative model without and with response style parameters (takes pretty long!!!) m.GLES20 <- multordRS(f.GLES, data = GLES17, model="cumul", control = ctrl.multordRS(opt.method = "nlminb", cores = 6, RS = FALSE)) m.GLES2 <- multordRS(f.GLES, data = GLES17, model="cumul", control = ctrl.multordRS(opt.method = "nlminb", cores = 6)) m.GLES20 m.GLES2 plot(m.GLES2, main = "Cumulative model") ```