I agree with Pat about causality, because everything I described was based on Winnie's description of which variables were the independent and which were the dependent, but assigning the variables to those roles has to be based on theory. In other words, there is a fundamental assumption here that perception of career stagnation predicts job performance as an outcome.

As for instrumental variables, that is a rather complex topic that probably goes beyond the kind of analyses being done here.

The attached document should address the issue you discuss. Also look at sampling attrition and under-sampling

The main problem with small sample size is that your statistical tests will lack "power" -- which means that you could easily miss some effects that would be significant with a larger N. One common solutions to use a lower alpha value, such as .10 rather than .05, to determine the effects that you consider worth examining.

In general, there should be no problem using regression, where the time-2 value is the DV and the time-1 value is included in the list of IVs. Note, however, that no method including SEM will determine causality, that has to be a matter of theory.

There are some interesting posts on this site which address the issues you raise

https://www.researchgate.net/post/What_are_the_Longitudinal_Data_Analyses_Options_for_just_Two_Time_Points

Thank you all for your quick responses! They have been really useful. I will have a look at them before determining my method for analysis.

Longitudinal survey designs are designs that assess subjects on two or more occasions with the same or similar instrument. They examine stability, development, or change in the subjects across a span of time.

Change or stability can be measured by getting the difference of the variables' means (for ratio/interval measures) between time 1 and time 2, and the difference in frequencies (for nominal measures)  of the variables between time and time 2. If your sample is probability you can proceed to Z test of difference between sample (paired or independent).

There could be different kinds of samples.

Panel design. It is a design where data are collected at different point in time from the same subjects (called panel).

Trend design. It is a design where a new sample is drawn at each measurement period to keep up with changes that may have occurred in the general population.

Cohort design. It is a variation in trend design in which specific subpopulations, or cohorts, are examined as they change overtime. A cohort is a group of people that have a certain characteristic in common, such as being born in the 1950, graduating from college in 2005, or marrying between 1990 and 2000. The same population is involved throughout the research but a fresh sample is selected every time data are gathered.

Could you please elaborate on what you mean by direction of causality?

I hope this helps.

Hi Eddie,

Thanks so much for your help! I'm doing a panel design, in which the same people are asked to respond to the exact same questionnaire at two time points. We are actually in the middle of collecting the third wave but not very sure how many responses we will have in the end (whether we will have enough for analysis, and to answer our research questions).

For my research, my IV is people's perception of career stagnation ( for instance perception of lack of promotion within their organisations), and the DVs are job performances. There's been studies out there that shows a negative relationship between the two, so we are testing whether career stagnation(Time-1) leads to poorer performance (Time 2). But, some say it may be poorer performance in the first place that leads to career stagnation (not being promoted because of poorer performance, and hence having a stagnated career), so I would like to test that too. This was what I meant by direction of causality. I hope this is the right way to express this?

Thanks again for your comments and help!

Winnie

Winnie,

Panel designs increase power relative to single-time designs for a given sample size. In other words, more data points per respondent can help compensate for a modest sample. You do need to carefully consider the issue of attrition, as Daryn brought up. If you are comfortable with the MCAR (testable) or MAR (not testable) assumption, either has methods that are essentially transparent to implement in almost any path software without introducing bias, even if attrition is relatively high at time 3.

That said, many longitudinal methodology researchers would not consider two time-points "longitudinal" in terms of the methods you'd apply, but start at three as a minimum. Two greatly limits your options.

Pat

The classic approach in a regression analysis would be to begin by entering the wave-1 measure of the dependent variable (job performance) and then assessing the effects of additional wave-one variables on top of that. In other words, you would be analyzing change in the dependent variable, which is basically the same as the extent to which poor performance at time-1 affects poor-perfomrance at time-2. If the regression coefficient is positive, this means that those with poor performance in the earlier wave had even worse performance in the later wave (and equivalently, that those with good performance earlier had even better performance latter).

If you next enter perceived stagnation at wave-one, this will test its influence on change in job performance, above and beyond the effect of the wave-one level of performance. If the coefficient is negative, this will mean that those who initially perceived stagnation were like to have declines in performance in the second wave, regardless of whether they were high or low performers in the first wave.

David describes the classic approach quite well.

I'll add, though, that it cannot disentangle causal direction, especially in an observational study. You might have some success with an instrumental-variable approach.

Pat

I agree with Pat about causality, because everything I described was based on Winnie's description of which variables were the independent and which were the dependent, but assigning the variables to those roles has to be based on theory. In other words, there is a fundamental assumption here that perception of career stagnation predicts job performance as an outcome.

As for instrumental variables, that is a rather complex topic that probably goes beyond the kind of analyses being done here.

Winnie, relationship indeed shows direction but not necessarily causal direction. This is because causality can only be investigated in an experimental design, where there is an experimental group, a control group and a treatment.