 Yleensä ymmärtää ympäristöä ja ymmärtää, miten ympäristöä, algoritma tai data-augumentation algoritma toimii, on useita ymmärtää ympäristöä, kun käytetään nämä teknikäyttöä. Täällä on tietysti minkälaista ympäristöä, mutta tämä on ympäristöä, jota käytetään user-manuella. Täällä on useita data, koska ympäristöä, että user-manuella on useita ympäristöä ja on useita ympäristöä, mutta tämä on useita ympäristöä, jota käytetään ympäristöä, jota ei ole ennen, ja hän voisi aurうん attacks flavored unusual manual olevan ymmärtää�� Japan tanustajoulua. Se onać use Typical To- strings funktioniertia minkää, kuinka hän hän mukaistaa ympärisöä ympäristöä. This is better understood through X-samples, so if you have, let's say, three X-variables, X1, X2 and X3, then you have a Y-variable and you are missingness only in the Y-variable. You can impute, let's say, 10 data sets and there are two ways of doing it. We can impute in the long form, which means that we create 10 new copies of all the variables including also those with no missing data. So if we start with 100 observations, we impute 10 copies of data, then in the end we have a larger data set with 1000 observations because we have 10 copies of 100 observations. So that's the long form. You can also impute in wide form, which means that we just generate new copies of the Y-variable that has the missing data. In the end we have 10 Y-variables, 3 X-variables and 100 observations instead of having these 1000 observations and just one Y-variable. So what's the advantage of either way? The traditional way of thinking about imputation is that you generate copies of the full data set. But if you have only a limited number of variables with missing data, that is wasteful and if you have a large data set you might run into memory issues. But that's probably less of a concern for most researchers, but for very large data sets that might be something that you need to consider. So understanding which form you want to impute in is the first decision that you do. The next decision or the next thing that you do is to explore the data. So building up a data imputation model is an iterative task, so you need to consider each variable at the time, whether it's imputed or not, what kind of model you use for imputation. And there are two things that you should do regularly. One is to describe your imputation model. So which variables are imputed, which are not, what is the functional form for one variable, what's the functional form for other variable. And this is something that our status in my describe will do you. Another thing that you need to do is to understand the patterns of missing data. So understanding the missingness before imputation and after imputation is useful. So you might start building your imputation model from ground up, imputing just a few variables at the time and then then exploring the data and or another alternative would be to build the full imputation model at once. Going forward with this gradual approach is probably easier if you have any convergence problems in the imputation instead of going with the full imputation model. So this is the general principle, if you have a large model that is problematic, then start with the smaller part and see if that is problematic and then incrementally build it and that will help you to understand what the problem is about. So you need to check the missing data patterns after imputation and before imputation and you need to regularly think about and inspect your imputation model. So these are the two things that you need to do and now let's take a look at how you actually specify the imputation model. You need to classify variables into different categories and importantly you need to tell your statistical software which variables are imputed. So not all variables should be imputed and the cases where you probably shouldn't impute are for example if you have a categorical variable and then you have dummy variables generated based on that category. You probably want to impute the categorical variable but not the dummies because there is a functional relationship between the dummies. If one is one, then the others must be zeros. The same thing if you have interactions, interactions are products of variables, you should probably impute the original variables but not the product and so on. So if you have auxiliary variables, they need to be registered because we are not generally interested in imputing values for those but we use them to help in the imputation process. And once we have built our imputation model, we need to print it out and go through it and see if it makes sense. Then the next step is the actual imputation. So you run the imputations and once you have run the imputations, then you need to generate what are called passive or non-imputed variables. And these will be transformations, interactions, dummy coding and so on. So any functional relationships between variables, you need to recreate these so called passive or non-imputed variables after the input days. Once you have done all these registered variables that you want to impute, imputed the data, generated the passive variables and throughout this process explored the missing data pattern and verified that the imputation model makes sense by printing it out, then the final step is that you run estimation within the multiple imputation framework. The idea, the reason why we want to estimate within the multiple imputation framework is that not all statistical software would just give it the imputation data sets understand that those data sets have been imputed and we need to tell the command to run multiple times instead of running once for all the data sets. So this is what the imputation estimation does and it also aggregates the results. So instead of taking all the imputed data sets and running one regression analysis, we need to run one regression analysis for each imputed data set and then aggregate the results taking into account that the standard errors need to be adjusted. And this is what the imputation estimation states does. Imputation generally should be done after data exploration. So you should explore the data first, understand the missing data pattern first, but doing some data exploration using the imputed data sets might be useful as well. For example, inspecting correlations, inspecting missing standard deviations after the imputed data sets is useful. Also if you are running, if you are reporting the standard deviations means and correlations in a paper, then you might want to do that table after the imputation process based on the imputed data sets because those imputed data sets are more descriptive of what you are actually doing. So this is the workflow and basically in the estimation stage you can estimate whatever things you would estimate using raw data, doing diagnostics and other things, the same thing as with the original model. If you have a regression model, it probably doesn't make sense to do all the regression post estimations for every possible data set, but instead you probably should just take one or a few of those data sets for diagnostics.