Loss leader item definition I've recently encountered the term "loss leader" for items. The definition is pricing an item at a discount for the purpose of increasing overall revenues. 

One example is Sony selling the PS4 at a loss in order to take more market share, which gain more profits via game sales.

Another example is grocery stores selling items on sale so that customers have a reason to visit the store, and then hopefully buy other items.

My question is: can this definition be extended to businesses that deal with data? For example, selling an online service at a discount to customers for the purpose of collecting data, and then selling that data to marketing firms for a profit.

Is that also an example of a loss-leader item? Or is there a more accurate example?
"Loss leader" is a term primarily from marketing. It is occasionally used by economists, but not in a formal way because its definition is insufficiently precise. 

To see why we have to be careful, it is useful to think about the economic principles underlying the three examples you mentioned. I do this below, but the ;tldr version is that the business model for selling data follows a totally different economic logic and even grocery stores vs playstations follows slightly different logic.



The grocery store example is probably the closest thing to what would commonly be understood as a loss-leader. The reason this strategy works is because consumers face some kind of friction that makes them disproportionately prefer one-stop shopping to visiting many stores (e.g. becoming informed about different stores is costly, switching stores in the middle of a shop is costly, etc.). The fact that consumers don't want to go to many stores means that once they are attracted into a store by a low price, they can be exploited with higher prices on other goods. To reiterate: note that this business model is driven by a feature of consumers' behaviour (search/shopping frictions).



The Playstation example follows a slightly different logic, similar to the razord and blades model mentioned by others. The key factors here are: (1) products are complements—we have two types of good (games consoles and games, or razors and blades) that only work if they are consumed together. (2) products are imperfectly compatible (I can't use Playstation games in an XBox). 

Now, suppose I bought a Playstation and then decided the games were too expensive and I would prefer switch over to XBox. This would require that I buy a new games console, which is expensive—so I will tend to be unwilling to switch to a different platform. This is just like the grocery store example: we have a situation where consumers are unwilling to switch from one supplier to another. Just like that example, firms offer a low introductory price to initially attract consumers, only to later exploit them once they are locked-in.

But note here that the switching frictions are not an intrinsic property of consumer behavior like in the earlier examples, but rather are now driven by the properties of the products themselves (complementarity and incompatibility). We have therefore identified two distinct sets of conditions under which this kind of pricing strategy might be attractive to a firm: either consumers are intrinsically reluctant to switch or they can be made so through design and compatibility choices.



What about businesses that offer free services in return for data? Here the underlying economic logic is completely different to the other two cases. These are typically examples of so-called two-sided markets. A two-sided market is a market in which a central intermediary (called a "platform") matches people from two distinct groups. In this particular example the two sides will be consumers and marketing firms, and the job of the platform is to bring the two together so that new value can be unlocked through the exchange of data.

Two-sided platforms typically involve a chicken and egg type problem because in order for the platform to function it is necessary to make sure both groups are on board (a heterosecual dating site that attracts only men won't be very useful!). The usual solution to this problem is that one of the two groups is subsidised (e.g. allowed to join the platform for free or at reduced cost). Once that group joins, the platform becomes more attractive to the other group, who can be charged a higher price. A classic example of this is nightclubs, which would often run "ladies nights" (low price admission for females,) thus ensuring many females enter the club. Once the club is full of females, it becomes much easier for the club owner to charge a high admission fee to men. Similarly, firms like Facebook subsidise consumers (with a free service) to get as many consumers on board as possible, so that the firm is able to extract as much value as possible from the other side of the market (selling data to marketing firms).

Note that the underlying economic mechanism here is different from the other cases. Those examples were about creating frictions to lock-in consumers, so that those same consumers could be charged a high price. Two-sided pricing is about offering a low price to one group in order to get them on board so that a totally different group of consumers can be charged a high price.



Final note: games consoles are also two-sided markets (they serve both gamers and game developers and must get both on board to be successful). So a bit of the two-sided logic applies there too: Playstations are sold below cost to gamers to get lots of gamers onto the platform because this allows Sony to maximise revenues from the royalty fees paid by game developers, as well as revenues from selling games to consumers.