Yes, Adspert supports all attribution models from AdWords:
Last click: Gives all credit for the conversion to the last-clicked ad and corresponding keyword.
First click: Gives all credit for the conversion to the first-clicked ad and corresponding keyword.
Linear: Distributes the credit for the conversion equally across all clicks on the path.
Time decay: Gives more credit to clicks that happened closer in time to the conversion. Credit is distributed using a 7-day half-life. In other words, a click 8 days before a conversion gets half as much credit as a click 1 day before a conversion.
Position-based: Gives 40% of credit to both the first- and last-clicked ads and corresponding keyword, with the remaining 20% spread out across the other clicks on the path.
Data-driven: Distributes credit for the conversion based on past data for this conversion action. (This is only available to accounts with enough data).
A change in the attribution model might have a big impact on your performance. Please check the outcome carefully. In case of doubt, please contact us.
You will find further information regarding attribution models at the AdWords Help Center: Beyond Last-Click Attribution: Google Best Practices.