I am sorry but I do not understand your question but it is perfectly possible to get these difference between cross-sectional and longitudinal effects;. This paper considers the issue - although you might not know that given the title. It is possible to use group mean centering in a random effects model to estimate both types of effect in a single model

Article Understanding and misunderstanding Group mean centering: a c...

Dear Manali,

It is not a matter of cross sectional or panel data nature, rather the robustness of the model results. If the cross-sectional data are generated from the random sample and asymptotically normally distributed; well specified and qualifies all the pertinent robustness checked tests, there is no reason that we would not trust the results. However, we have to be equally recognize the advantage of panel data, which can have obvious advantages over cross sectional data: large sample size, controlling time invariant (fixed effects) which may biased results.

So, it is up to the researcher to scrutinize and identify which results are robust.

Kidanemariam

I am sorry but these designs/analysis are tackling two different questions - cross-sectional is about the enduring relation; longitudinal is about the changing relation.

And I have no idea why you invoke random samples and asymptotically normal distributions - these methods now routinely handle clustered (beyond occasions nested within individuals) and stratified designs and non-normal distribution eg Bernoulli, binomial , Poisson, NBD Gamma.....

Thank you Kelvyn and Kidanemariam for your generous response.

Model wise, the panel data is a better model. We have checked its robustness as well.

I am interested in further invoking the data so that some serious hindsight can be fetched out. If you could recommend any paper on fixed effect as I shall be looking into what was the influence of fixed effect in my data sample.

Have a read of these papers as to why you can get more out of a random effects - within and between analysis - than a fixed effects

Article Fixed and Random effects models: making an informed choice

Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...

and for a feeling of the debates

https://en.wikipedia.org/wiki/Kelvyn_Jones

the section

"He (with colleagues) has challenged the 'gold standard' that fixed effects should be the standard approach to the analysis of Panel data and that a Hausman test is an appropriate way of choosing between a Fixed effects model and a Random effects model. .................."

I am extremely thankful to you, Kelvyn.

I am likely to reach out to you for further discussion.