Invited talk, IMPS Prague, July 2024. Abstract: "In the last decades, Psychometrics Island has been bustling with creativity and productivity, resulting in beautiful models such as factor and network analysis. These models have arrived via air mail on Psychology Mainland, often with cryptic instruction material and little information about how models ought to be used. Perhaps it is not surprising that much of the applied literature using these models falls short of sound theory building and testing. For instance, researchers commonly conflate statistical and theoretical models, and there is an over-reliance on fit indices to adjudicate between models. Latent theories are common, when authors use implicit beliefs or causal assumptions to guide inferences. Generally, much of the literature looks as if researchers are baking psychometric cakes following the same recipe over and over again, without generating insight or knowledge. In this talk, I discuss these problems with a focus on factor and network models. I conclude that psychometricians ought to be aware of these problems that threaten the validity of findings, and that you play a crucial role to mitigate and prevent them. We need you, not only on Psychometrics Island, but also on Psychology Mainland."