[Hui SHI]

I do not know how the authors of these articles calculated the BIC. Without extra information, their choices seem wrong. When you base your decision on the AIC or BIC as reported by the official Stata command estat ic, you select the model with the smaller (i.e. more negative) value of those criteria.

Thanks for your reply.

Welcome more experts express your view on this question: how to choose one best model when BIC & AIC are negative value(-)

[Sebastian Kripfganz]

It is not a matter of one's "view". It is just a question how the AIC/BIC was computed. When computed in the normal way, my earlier statements stand.

[Hui SHI]

It is not a matter of one's "view". It is just a question how the AIC/BIC was computed. When computed in the normal way, my earlier statements stand.

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In this paper: Bayesian Estimation and Model Selection in Group-Based Trajectory Models, there are computational methods of LL, BIC, and some equations. I am a medical student, so it is hard for me to understand computational methods. I can only write code and run the model.

Thanks for updated answers.

[Tom Scott]

help estat ic

The more negative value indicates a better fitting model. When in doubt, look at the formula, not at what other researchers have done in the past. Unless its a really good journal

[Hui SHI]

help estat ic

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The more negative value indicates a better fitting model. When in doubt, look at the formula, not at what other researchers have done in the past. Unless its a really good journal

The BIC in group-based trajectory modeling is different.

[Gabor Mihala]

BIC values closer to zero (as opposed to closer to negative infinity) are favoured in group-based trajectory modelling, to select the 'best' model.

References:
Jones, B. L., Nagin, D. S., & Roeder, K. (2001). A SAS Procedure Based on Mixture Models for Estimating Developmental Trajectories. Sociological Methods & Research, 29(3), 374–393. https://doi.org/10.1177/0049124101029003005
Sweeten, G. (2014). Group-Based Trajectory Models. In: Bruinsma, G., Weisburd, D. (eds) Encyclopedia of Criminology and Criminal Justice. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5690-2_479
J. Salonen, H. Tikanmäki, T. Nummi; 2019; Using trajectory analysis to test and illustrate microsimulation outcomes; International Journal of Microsimulation; 12(2); 3-17. DOI: 10.34196/IJM.00198
Mésidor, M., Rousseau, MC., O’Loughlin, J. et al. Does group-based trajectory modeling estimate spurious trajectories?. BMC Med Res Methodol 22, 194 (2022). https://doi.org/10.1186/s12874-022-01622-9
Marie-Pier Vézina & François Poulin (2019) Investigating civic participation developmental trajectories among Canadian youths transitioning into adulthood, Applied Developmental Science, 23:1, 59-73, DOI: 10.1080/10888691.2017.1301816

[Sebastian Kripfganz]

BIC values closer to zero (as opposed to closer to negative infinity) are favoured in group-based trajectory modelling, to select the 'best' model.

Sorry, but this statement is just wrong and not supported by your references. If the BIC is defined as in post #19 above, the smallest (most negative) value is preferred. If the BIC is defined as in post #20, the largest (most positive) value is preferred. The latter equals the former multiplied by -2, and seems to be the way it is computed in the literature on group-based trajectory modeling. The former is the way it is reported in Stata.

[Hui SHI]

Sorry, but this statement is just wrong and not supported by your references. If the BIC is defined as in post #19 above, the smallest (most negative) value is preferred. If the BIC is defined as in post #20, the largest (most positive) value is preferred. The latter equals the former multiplied by -2, and seems to be the way it is computed in the literature on group-based trajectory modeling. The former is the way it is reported in Stata.

Greeting,

Thanks for this debate, I have ever asked many experts. I would like to provide some relaible evidence about this discussion I posted.

Please check the attachment. It come from the textbook: Group-based modeling of development

Nagin, Daniel S., 1948- / Daniel S. Nagin.
2005

the largest BIC score, the best the model fit

[Leonardo Guizzetti]

The BIC in group-based trajectory modeling is different.

Respectfully, it is not computed any differently from the standard way, it is just a scaled version. Just to spell it out, the usual formula is shown for example -help estat ic- and comment #19 can be rearranged with some simple algrebra to the form shown in #23.

BIC = -2 ln(L) + k ln(N)
BIC = -2 [ ln(L) - 0.5 k ln(N) ]

It seems that the custom among group-based modelers is to express BIC as a positive value, discarding the factor -2.

Referring to comments #4 and #22, if the factor -2 is included, then BIC is negative and the more negative is the better model fit. If the factor -2 is omitted, then BIC is positive and the more positive value is the better model. In both cases, the value further from zero is the better fit.

[Sebastian Kripfganz]

Referring to comments #4 and #22, if the factor -2 is included, then BIC is negative and the more negative is the better model fit. If the factor -2 is omitted, then BIC is positive and the more positive value is the better model. In both cases, the value further from zero is the better fit.

I am afraid, the last sentence in this statement is still not entirely accurate. In the conventional version implemented in Stata, when more negative values of the BIC are preferred, it is possible that the BIC turns out to be positive; e.g., comparing a model with BIC = -1 to BIC = +2, we would still prefer the first model with the more negative BIC, even though it is closer to zero. For the scaled version in group-based trajectory modeling, the same arguments apply with reversed sign.

[Leonardo Guizzetti]

Thank you for the correction, Sebastian.

[Rosie Huynh]

Hi,
I'm new to trajectory modeling and have the same issue as the original question #1. I've gone through the replies but still can't get it to work correctly.
In my case, I have three domains that I want to model trajectories for. For example, with family factors, I started with 1 group and a linear order (1). However, whenever I adjust anything - such as adding more groups or increasing the order - the BIC increases. The BIC starts from a negative value and becomes positive as I make changes. This same pattern happens across all three domains.
If "the lower the BIC, the better the fit" is the guiding principle, does this mean I can’t perform trajectory modeling with my dataset? It doesn’t seem to make sense to me.
Thank you