Big Five was derived through EFA (exploratory factor analysis) and then tested through many a CFA (confirmatory factor analysis) studies, so I'm guessing you're looking for something similar in the realms of political spectrum.
Any such test is only as relevant as the questions it fathoms to ask, i.e. you may entirely miss a dimension if it didn't occur to you ask anything about it. There were early attempts to base political spectrum questionnaires based on actual political statements found in the press, e.g. Eysenck's--compare to basing Big Five on adjectives existent in various languages--this was one of the two avenues for its development.)
Hans Eysenck began researching political attitudes in Great Britain. He believed that there was something essentially similar about the National Socialists (Nazis) on the one hand and the communists on the other, despite their opposite positions on the left–right axis. As Hans Eysenck described in his 1956 book Sense and Nonsense in Psychology, Eysenck compiled a list of political statements found in newspapers and political tracts and asked subjects to rate their agreement or disagreement with each. Submitting this value questionnaire to the same process of factor analysis used by Ferguson, Eysenck drew out two factors, which he named "Radicalism" (R-factor) and "Tender-Mindedess" (T-factor). [...]
Eysenck's dimensions of R and T were found by factor analyses of values in Germany and Sweden, France and Japan.
In further research, Hans J. Eysenck refined his methodology to include more questions on economic issues. Doing this, he revealed a split in the left–right axis between social policy and economic policy, with a previously undiscovered dimension of socialism-capitalism (S-factor).
While factorially distinct from Eysenck's previous R factor, the S-factor did positively correlate with the R-factor, indicating that a basic left–right or right–left tendency underlies both social values and economic values, although S tapped more into items discussing economic inequality and big business, while R relates more to the treatment of criminals and to sexual issues and military issues.
So the methods used for developing political factors were no so unlike although surveying the press is likely a less stable method (temporally) than surveying languages.
On the other hand, quite a few political science researchers have presupposed some factors theoretically and just tested them. Or not even tested them. I suspect the rather popular Nolan chart on which a lot of the "compasses" out there on the web are based on wasn't subject to much validation. Actually in order to speak of validation, one needs questionnaire and not merely a chart (or set of dimensions).
Another important issue is to ask what do you want to use these factors for. As Philipp's comment rightly points out, the factors one may posit or even identify via EFA may or may not be relevant or salient to some actual politics issue, like some particular election outcome.
Also, as it's pointed out e.g. in Big Five research (which also has finer-grained facets), broad dimensions may not satisfactorily explanatory for some particular issue (e.g. like fit for a specific job, in the case of personality). Depending how sensitive you want your analysis to be on some dependant variable, you may have consider more [sub]factors. E.g., in the case of Irish politics:
In the Irish case, using data from the 2002 Irish National Election Study
(INES), Marsh et al. (2008: 41) found that fully six dimensions were required
to adequately capture the variation in voters’ issue preferences. The issues
that constitute a single cultural dimension in some other contexts were
found to form three separate dimensions in the Irish case: a secular-liberalism
versus a religious-conservatism dimension; an environmental dimension and
a dimension related to European integration. Furthermore, they found that
positions on economic issues were not constrained by a single left–right
dimension, but rather formed two separate dimensions: one relating to the
role of the state in the economy, and the other relating to redistribution.
The sixth dimension identified was a distinctly Irish one related to the question of Northern Ireland.
separate dimensions can adequately account for voters’ opinions on a
diverse range of policy issues that were salient in the 2016 general election.
These are the economic, cultural, religious and austerity dimensions. The
first three of these ideological dimensions relate to more or less perennial
issues and are likely to have continued relevance in Irish politics in the
years to come. The long-term importance of the austerity dimension is less
But for some other purposes as single dimension may explain a lot e.g. in the case of Taiwan parties:
Moral foundations theory provides a framework for understanding the traditional liberal–conservative dichotomy in political factions. Typically, factions on the liberal side are more concerned with individualizing foundations—including care/harm and fairness/cheating—for the protection of individual rights and welfare whereas factions on the conservative side are concerned with both individualizing and binding foundations—including loyalty/betrayal, authority/subversion, and sanctity/degradation—for the maintenance of existing social ethics. Our research extended this framework to the analysis of Taiwanese political factions, which are not distributed conspicuously along the liberal–conservative line but instead on whether Taiwan should become a legally independent state or unify with the People's Republic of China (Mainland China). Our results indicate that despite the scarce use of the terms liberal or left and conservative or right in common communication, a liberal–conservative dimension underlies the Taiwanese political spectrum. Specifically, supporters of Taiwan independence exhibit liberal‐like moral concerns whereas supporters of China unification and the status quo demonstrate conservative‐like moral concerns. Moreover, indirect effects exist through moral foundations from political factions to stances on social issues; this is especially prevalent in the case of Taiwan independence camp's clear support for the legalization of same‐sex marriage, a stance resulting from anti‐authoritarian moral and political characteristics.
So the question whether some classification is "scientific" doesn't have a single answer. It's more useful to ask if a classification is explanatory for some stated purpose.
Interestingly enough, I did find one paper that finds the social dimension mostly irrelevant for party identification in the US, with the [Nolan-style] economic dimension dominating.
One dimension is the long-standing economic dimension, which concerns
government spending, taxes, and redistribution policies. A second dimension,
which has become salient only in more recent decades, focuses on social and
cultural issues such as abortion and gay rights. [...]
Thus while social issues have clearly
become a more salient dimension of American politics in recent decades—as seen
in their growing effect on voters’ ideological identifications — when it comes to
partisanship, traditional concerns about the role of government and economic
issues loom supreme.
They do find some differences on elections turnout based on the social dimension though.