# Generating synthetic data sets Generates synthetic version(s) of a data set. Function `syn.strata()` performs stratified synthesis. ```r syn(data, method = "cart", visit.sequence = (1:ncol(data)), predictor.matrix = NULL, m = 1, k = nrow(data), proper = FALSE, minnumlevels = 1, maxfaclevels = 60, rules = NULL, rvalues = NULL, cont.na = NULL, semicont = NULL, smoothing = NULL, event = NULL, denom = NULL, drop.not.used = FALSE, drop.pred.only = FALSE, default.method = c("normrank", "logreg", "polyreg", "polr"), numtocat = NULL, catgroups = rep(5, length(numtocat)), models = FALSE, print.flag = TRUE, seed = "sample", ...) syn.strata(data, strata = NULL, minstratumsize = 10 + 10 * length(visit.sequence), tab.strataobs = TRUE, tab.stratasyn = FALSE, method = "cart", visit.sequence = (1:ncol(data)), predictor.matrix = NULL, m = 1, k = nrow(data), proper = FALSE, minnumlevels = 1, maxfaclevels = 60, rules = NULL, rvalues = NULL, cont.na = NULL, semicont = NULL, smoothing = NULL, event = NULL, denom = NULL, drop.not.used = FALSE, drop.pred.only = FALSE, default.method = c("normrank", "logreg", "polyreg", "polr"), numtocat = NULL, catgroups = rep(5,length(numtocat)), models = FALSE, print.flag = TRUE, seed = "sample", ...) ## S3 method for class 'synds' print(x, ...) ``` ## Arguments - `data`: a data frame or a matrix (`n` x `p`) containing the original data. Observations are in rows and variables are in columns. - `method`: a single string or a vector of strings of length `ncol(data)` specifying the synthesising method to be used for each variable in the data. Order of variables is exactly the same as in `data`. If specified as a single string, the same method is used for all variables in a visit sequence unless a data type or a position in a visit sequence requires a different method. If `method` is set to `"parametric"` the default synthesising method specified by the `default.method` argument are applied. Variables that are transformations of other variables can be synthesised using a passive method that is specified as a string starting with `~` (see `syn.passive`). Variables that need not to be synthesised have the empty method `""`. By default all variables are synthesised using `"cart"` method, which is `rpart` implementation of a CART model (see `syn.cart`). See details for more information on method. - `visit.sequence`: a character vector of names of variables or an integer vector of their column indices specifying the order of synthesis. The default sequence `1:ncol(data)` implies that column variables are synthesised from left to right. See details for more information. - `predictor.matrix`: a square matrix of size `ncol(data)` specifying the set of column predictors to be used for each target variable in the row. Each entry has value 0 or 1. A value of 1 means that the column variable is used as a predictor for the row variable. Order of variables is exactly the same as in `data`. By default all variables that are earlier in the visit sequence are used as predictors. For the default visit sequence (`1:ncol(data)`) the default `predictor.matrix` will have values of 1 in the lower triangle. See details for more information. - `m`: number of synthetic copies of the original (observed) data to be generated. The default is `m = 1`. - `k`: a size of the synthetic data set (`k x p`), which can be smaller or greater than the size of the original data set (`n x p`). The default is `nrow(data)` which means that the number of individuals in the synthesised data is the same as in the original (observed) data (`k = n`). - `proper`: a logical value with default set to `FALSE`. If `TRUE` proper synthesis is conducted. - `minnumlevels`: a minimum number of values a numeric variable should exceed to be treated as numeric during the synthesis. Numeric variables with only `minnumlevels` or fewer distinct values are changed into factors. If set to `1` (default) numeric variables are left unchanged unless they have only one non-missing value. - `maxfaclevels`: a maximum number of factor levels that can be handled. It can be increased to allow the synthesis to run but too large a value may cause computational problems, especially for parametric methods. - `rules`: a named list of rules for restricted values. Restricted values are those that are determined explicitly by values of other variables. The names of the list elements must correspond to the variables names for which the rules need to be specified. - `rvalues`: a named list of the values corresponding to the rules specified by `rules`. - `cont.na`: a named list of codes for missing values for continuous variables if different from the `R` missing data code `NA`. The names of the list elements must correspond to the variables names for which the missing data codes need to be specified. - `semicont`: a named list of values at which semi-continuous variables have spikes. The names of the list elements must correspond to the names of the semi-continuous variables. - `smoothing`: a single string specifying a smoothing method for all numeric variables in the data or a named list specifying a smoothing method to be used for selected variables. Available methods include: `"spline"` (recommended), `"rmean"`, `"density"`, and `""`). Smoothing can only be applied to continuous variables synthesised using `sample`, `ctree`, `cart`, `rf`, `bag`, `ranger`, `normrank`, `pmm` or `nested` method. The names of the list elements must correspond to the names of the variables whose values are to be smoothed. Smoothing is applied to the synthesised values. For more details see `syn.smooth`. - `event`: a named list specifying for survival data the names of corresponding event indicators. The names of the list elements must correspond to the names of the survival variables. - `denom`: a named list specifying for variables to be modelled using binomial regression the names of corresponding denominator variables. The names of the list elements must correspond to the names of the variables to be modelled using binomial regression. - `drop.not.used`: a logical value. If `TRUE` (default) variables not used in synthesis are not saved in the synthesised data and are not included in the corresponding synthesis parameters. - `drop.pred.only`: a logical value. If `TRUE` (default) variables not synthesised and used as predictors only are not saved in the synthesised data. - `default.method`: a vector of four strings containing the default parametric synthesising methods for numerical variables, factors with two levels, unordered factors with more than two levels and ordered factors with more than two levels respectively. They are used when `method` is set to `"parametric"` or when there is an inconsistency between variable type and provided method. - `numtocat`: a vector of numbers or names to indicate columns of `data` that are to be divided into groups to allow the grouped variables to be synthesised as factors. The target number of groups for each variable is specified by `catgroups`. After the grouped variables have been synthesised the numeric variables are synthesised from them by the method `syn.nested` and are placed in the same position in the synthetic data as in the original. The grouped variables are not stored in the synthetic data. If you want to keep the categorised values you should change the relevant variables in `data` before running `syn()` with the function `numtocat.syn()` - `catgroups`: An integer or a vector of integers of the same length as `numtocat` giving the target number of groups into which of the numeric variables is to be categorised. The function `group_var` from the `classInt` package performs the categorisation. - `models`: if `TRUE` parameters of models fitted to the original data and used to generate the synthetic values are stored. - `print.flag`: if `TRUE` (default) synthesising history and information messages will be printed at the console. For silent computation use `print.flag = FALSE`. - `seed`: an integer to be used as an argument for the `set.seed()`. If no integer is provided, the default `"sample"` will generate one and it will be stored. To prevent generating an integer set `seed` to `NA`. - ``...``: additional arguments to be passed to synthesising functions. See section 'Details' below for more information. - `strata`: a numeric vector with strata identifiers or a string vector with names of stratifying variable(s). - `minstratumsize`: minimum size of each stratum. - `tab.strataobs`: a logical value indicating whether a frequency table of the number of observations in strata in the original data set should be printed. - `tab.stratasyn`: a logical value indicating whether a frequency table of the number of observations in strata in the synthetic data set(s) should be printed. - `x`: an object of class `synds`; a result of a call to `syn()`. ## Details Only variables that are in `visit.sequence` with corresponding non-empty `method` are synthesised. The only exceptions are event indicators. They are synthesised along with the corresponding time to event variables and should not be included in `visit.sequence`. All other variables (not in `visit.sequence` or in `visit.sequence` with a corresponding blank method) can be used as predictors. Including them in `visit.sequence` generates a default `predictor.matrix` reflecting the order of variables in the `visit.sequence` otherwise `predictor.matrix` has to be adjusted accordingly. All predictors of the variables that are not in `visit.sequence` or are in `visit.sequence` but with a blank method are removed from `predictor.matrix`. Variables to be synthesised that are not synthesised yet cannot be used as predictors. Also all variables used in passive synthesis or in restricted values rules (`rules`) have to be synthesised before the variables they apply to. Mismatch between data type and synthesising method stops execution and print an error message but numeric variables with number of levels less than `minnumlevels` are changed into factors and methods are changed automatically, if necessary, to methods for categorical variables. Methods for variables not in a visit sequence will be changed into blank. The built-in elementary synthesising methods defined by conditional distributions include: - **ctree, cart**: classification and regression trees (CART), see `syn.cart` - **bagging, random forests, ranger**: methods using ensembles of CART trees, see `syn.bag`, `syn.rf`, and `syn.ranger` - **survctree**: classification and regression trees (CART) for duration time data (parametric methods for survival data are not implemented yet), see `syn.survctree` - **norm**: normal linear regression, see `syn.norm` - **normrank**: normal linear regression preserving the marginal distribution, see `syn.normrank` - **lognorm, sqrtnorm, cubertnorm**: normal linear regression after natural logarithmic, square root and cube root transformation of a dependent variable respectively, see `syn.lognorm` - **logreg**: logistic regression, see `syn.logreg` - **polyreg**: unordered polytomous regression, see `syn.polyreg` - **polr**: ordered polytomous regression, see `syn.polr` - **pmm**: predictive mean matching, see `syn.pmm` - **sample**: random sample from the observed data, see `syn.sample` - **passive**: function of other synthesised data, see `syn.passive` - **nested**: bootstrap sample within each category of the original grouping variable, see `syn.nested` - **satcat**: bootstrap sample within each category of the crosstabulation of all the predictor variables, see `syn.satcat` These methods use a group of variables that are synthesised together. They must always be together at the start of the visit sequence: - **catall**: fit a saturated log-linear model, see `syn.catall` - **ipf**: fit a log-linear model, defined by its margins, by iterative proportional fitting see `syn.ipf` The functions corresponding to these methods are called `syn.method`, where `method` is a string with the name of a synthesising method. For instance a function corresponding to `ctree` function is called `syn.ctree`. A new synthesising method can be introduced by writing a function named `syn.newmethod` and then specifying `method` parameter of `syn()` function as `"newmethod"`. In order to use `"nested"` sampling, `method` parameter of `syn` function has to be specified as `"nested.varname"`, where `"varname"` is the name of the grouped (less detailed) variable, the only one used in nested synthesis. A variable synthesised using `"nested"` method is excluded from synthesising other variables except when used for `"nested"` method. Additional parameters can be passed to synthesising methods as part of the `dots` argument. They have to be named using period-separated method and parameter name (`method.parameter`). For instance, in order to set a `minbucket` (minimum number of observations in any terminal node of a CART model) for a `ctree` synthesising method, `ctree.minbucket` has to be specified. The parameters are method-specific and will be used for all variables to be synthesised using that method. See help for `syn.method` for further details about the allowed parameters for a specific method. ## Returns The `summary` function (`summary.synds`) can be used to obtain a summary of the synthesised variables. An object of class `synds`, which stands for 'synthesised data set'. It is a list with the following components: - **call**: an original call to `syn()`. - **m**: number of synthetic versions of the original (observed) data. - **syn**: a data frame (for `m = 1`) or a list of `m` data frames (for `m > 1`) with synthetic data set(s). - **method**: a vector of synthesising methods applied to each variable in the saved synthesised data. - **visit.sequence**: a vector of column indices of the visiting sequence. The indices refer to the columns in the saved synthesised data. - **predictor.matrix**: a matrix specifying the set of predictors used for each variable in the saved synthesised data. - **smoothing**: a vector specifying smoothing methods applied to each variable in the saved synthesised data. - **event**: a vector of integers specifying for survival data the column indices for corresponding event indicators. The indices refer to the columns in the saved synthesised data. - **denom**: a vector of integers specifying for variables modelled using binomial regression the column indices for corresponding denominator variables. The indices refer to the columns in the saved synthesised data. - **proper**: a logical value indicating whether proper synthesis was conducted. - **n**: a number of cases in the original data. - **k**: a number of cases in the synthesised data. - **rules**: a list of rules for restricted values applied to the synthetic data. - **rvalues**: a list of the values corresponding to the rules specified by `rules`. - **cont.na**: a list of codes for missing values for continuous variables. - **semicont**: a list of values for semi-continuous variables at which they have spikes. - **drop.not.used**: a logical value indicating whether variables not used in synthesis are saved in the synthesised data and corresponding synthesis parameters. - **drop.pred.only**: a logical value indicating whether variables not synthesised and used as predictors only are saved in the synthesised data. - **models**: if `models = TRUE` a named list of estimates of models fitted to the original data and used to generate the synthetic values is returned from the `$fit` component of each method (e.g. `syn.cart()`). The list is ordered by the variables position in the data, and any models used to predict missing values are appended to the list. - **seed**: an integer used as a `set.seed()` argument. - **var.lab**: a vector of variable labels for data imported from SPSS using `read.obs()`. - **val.lab**: a list of value labels for factors for data imported from SPSS using `read.obs()`. - **obs.vars**: a vector of all variable names in the observed data set. When `syn.strata()` is used there are two additional components: - **strata.syn**: a factor variable or a list of factor variables containing stratum values for all observation units in `syn`. - **strata.lab**: a character vector of strata labels. Note also that when `syn.strata` is used most values of the items are matrices with each row corresponding to a stratum or lists with one element per stratum. ## Note See package vignette for additional information. ## References Nowok, B., Raab, G.M and Dibben, C. (2016). synthpop: Bespoke creation of synthetic data in R. **Journal of Statistical Software**, 74 (11), 1-26. tools:::Rd_expr_doi("10.18637/jss.v074.i11") . ## See Also `compare.synds`, `summary.synds` ## Examples ```r ### selection of variables vars <- c("sex","age","marital","income","ls","smoke") ods <- SD2011[1:1000, vars] ### default synthesis s1 <- syn(ods) s1 ### synthesis with default parametric methods s2 <- syn(ods, method = "parametric", seed = 123) s2$method ### multiple synthesis of selected variables with customised methods s3 <- syn(ods, visit.sequence = c(2, 1, 4, 5), m = 2, method = c("logreg","sample","","normrank","ctree",""), ctree.minbucket = 10) summary(s3) summary(s3, msel = 1:2) ### adjustment to the default predictor matrix s4.ini <- syn(data = ods, visit.sequence = c(1, 2, 5, 3), m = 0, drop.not.used = FALSE) pM.cor <- s4.ini$predictor.matrix pM.cor["marital","ls"] <- 0 s4 <- syn(data = ods, visit.sequence = c(1, 2, 5, 3), predictor.matrix = pM.cor) ### handling missing values in continuous variables s5 <- syn(ods, cont.na = list(income = c(NA, -8))) ### rules for restricted values - marital status of males under 18 should be 'single' s6 <- syn(ods, rules = list(marital = "age < 18 & sex == 'MALE'"), rvalues = list(marital = 'SINGLE'), method = "parametric", seed = 123) with(s6$syn, table(marital[age < 18 & sex == 'MALE'])) ### results for default parametric synthesis without the rule with(s2$syn, table(marital[age < 18 & sex == 'MALE'])) ### synthesis with ipf for all variables s7 <- syn(ods[, 1:3], method = "ipf", numtocat = "age") ### alternatively group the numeric variable before synthesis to save ### the grouped data rather than the numeric in the synthetic data set ods.cat <- numtocat.syn(ods, numtocat = "age", catgroups = 10)$data s8 <- syn(ods.cat[, 1:3], method = "ipf") ### stratified synthesis s9 <- syn.strata(ods, strata = "sex") ```

syn function