Many statistical procedures make the assumption that the data (observations) are independent and identically distributed (i.i.d.).

Often, however, this assumption is unrealistic and statisticians have developed numerous methods appropriate for situations when it is untenable.

For example, employee attitudes in one company are usually more similar within that company than to attitudes in another company. Hierarchical models (aka multilevel models) can be used to account for this lack of independence in the data.

Data may be correlated across time, too. For example, sales in one week are usually similar to sales in the preceding week. Many methods have been developed to account for autocorrelated data and are widely used in many disciplines.

Mixture models are useful when we cannot assume that one distribution applies to all observations. Some data are multimodal, for instance, and mixture models can account for this.

Note that we need not assume one distribution applies to all variables in our data. It is possible to model continuous, ordinal, nominal and count data simultaneously, for example. Hierarchical, time-series and mixture models can all be combined too, if necessary.

I have no idea how many ways there are to conduct a regression type of analysis. Hundreds would not be an exaggeration.

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